# Interpretation of Non-Clinical Data for Prediction of Human Pharmacokinetic Parameters: In Vitro-In Vivo Extrapolation and Allometric Scaling

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## Abstract

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## 1. Introduction

## 2. Theoretical Background for the Prediction of Clearance

#### 2.1. Physiological Clearance Concept

_{0-inf}is area under the concentration-time curve from zero to infinity. In this equation, the volume of distribution (V) does not need to be defined. In case of administration involving the absorption pathway, the dose is adjusted based on bioavailability (F).

_{el}, or k

_{10}) and V. This method assumes a defined compartment model. In this method, CL is calculated based on the following equation:

#### 2.1.1. Organ Clearance

_{out}is less than C

_{in}(C

_{out}< C

_{in}), in which C

_{in}and C

_{out}indicate drug concentration in artery and venous, respectively.

_{in}·Q − C

_{out}·Q = Q·(C

_{in}− C

_{out})

_{E}is drug concentration in the clearing organ. However, in a practical setting, the analysis of the actual drug concentration in the organ is impossible. Therefore, C

_{E}is substituted by C

_{out}which can be measured in a practice setting using the partition coefficient between C

_{E}and C

_{out}as shown in the equations below:

_{in}and C

_{out}and substituting these solutions into Equation (1), the final solution yields Equation (10) below. The detailed solving method has been represented in Rowland et al. [34]:

_{org}denotes the organ clearance.

_{el}K

_{P}V

_{E}is defined as intrinsic clearance (CL

_{int}); in other words, an intrinsic capability of a liver to remove a drug from the blood without any flow limitations. The unit of k

_{el}K

_{P}V

_{E}is identical to CL, and it is expressed by the following equation:

_{org}is a function of Q and CL

_{int}. There are two circumstances depending on the relative size of the two variables.

- The first situation is when the clearance capacity (i.e., CL
_{int}) exceeds the Q (CL_{int}>> Q). In this situation, Equation (12) collapses and transforms to Equation (13).$${\mathrm{CL}}_{\mathrm{org}}\cong \mathrm{Q},{\hspace{1em}\mathrm{if}\mathrm{CL}}_{\mathrm{int}}\gg \mathrm{Q}$$ - The second situation is when C
_{out}is a small fraction of C_{in}(i.e., when K_{p}is high, or ER is low). [34]. In this case, Equation (12) collapses in the following equation:$${\mathrm{CL}}_{\mathrm{org}}\cong {\mathrm{CL}}_{\mathrm{int}},{\hspace{1em}\mathrm{if}\mathrm{CL}}_{\mathrm{int}}\ll \mathrm{Q}$$

_{p}) or blood (f

_{b}). In practical settings, the calculation of protein binding and the analysis of drug concentration are usually performed with plasma. Interconversion between the free fractions in blood and in plasma is shown below:

_{B}and C

_{P}refer to the total drug concentration in blood and in plasma, respectively. H

_{ct}is the hematocrit with a value of 0.44 in humans [35] and C

_{RBC}refers to the drug concentration in red blood cells.

_{org}is expressed by the equation below by incorporating f

_{p}:

#### 2.1.2. Consideration of Enzyme Kinetics

_{H}) and enzyme kinetics is expressed by the equation below.

_{met}) in the liver is described by the Michaelis–Menten equation:

_{max}is the maximal rate of the reaction, C is the concentration of the substrate, and K

_{m}is the Michaelis constant. If both sides of Equation (18) are divided by C, then V

_{met}/C is the hepatic intrinsic clearance (CL

_{int, H}) as shown in the following equation:

_{m}is much greater than C. Thus, Equation (19) can be simplified into the following equation:

_{max}and K

_{m}are calculated. Then hepatic clearance is estimated by embedding the CL

_{int, H}into Equation (12).

#### 2.1.3. Hepatic Clearance Model

#### Well-Stirred Model

_{H}is described by Equation (5):

_{H}= Q

_{H}· ER

_{H}

_{H}is the hepatic blood flow (20.7 mL/min/kg in humans), and ER

_{H}is the hepatic extraction ratio. Since ER is dependent on Q

_{H}, CL

_{H}is not directly proportional to Q

_{H}. Typically ER decreases with increasing Q

_{H}[32]. Additionally, hepatic availability (F

_{H}) is calculated by the following equation using ER

_{H}:

_{H}, equations of CL

_{H}, ER

_{H}, and F

_{H}are simplified as the following equations:

_{H}, the equations of CL

_{H}, ER

_{H}, and F

_{H}are to be simplified to the following equations:

#### Parallel-Tube Model

_{H}is expressed by the following equation:

_{H}and Q

_{H}are known, the CL

_{int,H}is estimated by this model. Taking the natural logarithm of the Equation (30):

_{H}[41,42].

_{org}. However, in certain situations, the estimation of CL

_{H}differs between the two models. Pang and Rowland have shown these differences [43,44,45]. In their studies, using lidocaine with an ER of 0.99 or higher, a liver perfusion experiment was conducted in mice. Its metabolite profile is well described by the well-stirred model. The major differences between these two models are F

_{H}based on changes of Q

_{H}and oral bioavailability (F

_{po}). When a drug with high ER

_{H}(e.g., lidocaine) is administered via per oral (PO) route, its F

_{po}is expressed by the following equation:

_{PO}is associated with Q

_{H}. In a well-stirred model, F

_{PO}shows a linear relationship with Q

_{H}. However, in the parallel-tube model, F

_{PO}changes exponentially with Q

_{H}. By comparing the observed values with predicted values using these two models, the investigator can select the model that better explains the organ clearance. However, under practical experimental settings, it is hard to determine the model with a good fit prior to an investigation. Therefore, unless there is obvious evidence, most investigators use the well-stirred model based on the principle that models should be as simple as possible, but not simpler [40,46].

#### Distributed Model and Dispersion Model

^{2}is an estimated parameter used to express variance for each sinusoid in the whole liver [52]. In the distributed model, the mixing of blood in the sinusoids is incorporated into flow rates and path length. The degree of mixing is defined by the dispersion number D

_{N}which is estimated in this model. When D

_{N}→ ∞ or D

_{N}→ zero, the dispersion model is collapsed in the well-stirred model and the parallel tube model, respectively. The variable ‘a’ in the dispersion model is equal to (1+4R

_{N}D

_{N})

^{1/2}, where the efficiency number of R

_{N}is equal to f

_{p}·CL

_{int,H}/Q

_{H}.

## 3. Prediction of Human Clearance Using IVIVE Method

#### 3.1. IVIVE

_{m}, V

_{max}, and k

_{in vitro}). The IVIVE method has been improved since its introduction by Rane et al. [59]. Scale-up of in vitro data to in vivo is performed by analyzing the correlation between in vitro and in vivo data or applying physiological correction factors. Many investigators have tried to improve the accuracy of prediction (Table 2).

#### 3.1.1. Empirical IVIVE Model

_{H}using in vitro hepatocytes and rat microsomes data by Houston [60]. In that study, the basic principal and process of IVIVE were presented. The physiological scaling factor was investigated. Results indicated that this simple scaling factor yielded adequate evidence supporting IVIVE.

_{H}. A scaling factor in Equation (41), shown in Table 2, was estimated using non-linear iterative least squares, which is not a fixed value. The predicted ER

_{H,pred}and intrinsic in vitro clearance (CL

_{int, in vitro}) had a good relationship. In this method, no protein binding was considered, resulting in overestimation of ER

_{H,pred}values of highly bound drugs. Nevertheless, the PK parameters of a few highly bound drugs, such as bosentan and lorazepam, were estimated with good agreement. The authors suggested that such discrepancy was attributed to the differences between the relative binding rate of the drug in the plasma and in hepatocytes, and/or its relative [61]. However, the overall predictability of human PK parameter was improved by applying a precise scaling factor, which plays a key role in the IVIVE method.

#### 3.1.2. Correction Factor of IVIVE Model

#### Protein Binding Factor

_{int, H, human}) using the in vitro half-life (t

_{1/2}) to incorporat non-specific binding factors to microsomes (f

_{u,mic}) and/or the f

_{p}. Twenty-nine drugs were classified according to their chemical property (i.e., basic, neutral, and acidic compounds). Generally, the basic compounds tend to have a large extent of binding. Results showed that human CL of neutral and basic compounds was adequately predicted with or without binding factors. However, in case of acid compounds, excluding binding factors, human CL values were predicted with a high degree of error.

_{int}was also investigated by Austin et al. [63]. In their work, rat liver microsomes were used as an in vitro system. Their results showed that the CL

_{int}was dependent on microsomal concentration. However, this relationship can be ignored when f

_{u,mic}is considered. The authors also found that f

_{u,mic}was correlated with lipophilicity. Based on these results, the authors formulated an equation for the calculation of f

_{u,mic}based on the physicochemical properties of drugs. Equation (36) can be used to calculate f

_{u,mic}as follows:

_{7.4}stands for the partition coefficient between octanol-0.02 M phosphate buffer (pH 7.4 at 20 °C). The logP is equal to the logD

_{7.4}for compounds designated as neutral and the logP is also calculated using the following equation:

_{u,mic}values are high enough to be ignored in the prediction of clearance. However, the few compounds with high microsomal binding should be considered to accurately predict the in vivo clearance. Therefore, when basic knowledge of the compound of interest is lacking in the early stage of drug discovery and development process, incorporating f

_{u,mic}is a preferable way to predict in vivo situations.

#### Animal Scaling Factor

_{int, in vivo}divided by CL

_{int, in vitro}to improve the human CL

_{int, in vivo}. This scaling factor is similar across species, since it depends on the compound itself. When the animal scaling factor in a rat or a dog was not considered, the average fold error increased (from an average two-fold to four-fold error). These results indicate that the scaling factor of each drug is conserved across an inter-species system. However, an animal scaling factor is difficult to use in the absence of adequate information for various species.

#### 3.1.3. Inter-Individual Variability (IIV) in the IVIVE Method

_{H}by IVIVE is generally limited by IIV, most likely due to drug metabolizing enzymes [74]. Several studies have reported the substantial differences in CYP expression and significant differences in the activity of different CYP isoforms in HLM [68,75,76]. The potential variation in the abundance of protein expression in relevant organs can be incorporated into IVIVE [77].

_{int, in vivo}from CL

_{int, in vitro}. Generally, a value of 45 mg/g liver [60] originally obtained from rat data, or 52.5 mg/g based on hepatocyte data reported in the literature via back calculation, is commonly used as MPPGL. Since the pharmacogenetic data of laboratory animal models are less than those of humans because of their genetics and environment, the variation in MPPGL of humans may be greater than that of rats [78].

#### Microsomal Protein Content and CYP Abundance

_{int, in vivo}if data are derived from microsomal protein [51]. Carliel et al. [67] have investigated diazepam as a model drug with high clearance. Its CL

_{int, in vivo}is 160 mL/min/SRW, where SRW refers to standard rat weight of 250 g. Microsomal content was adjusted by treating phenobarbital and dexamethasone as CYP inducing agents. The scaling factor calculated from Equation (49) was used to estimate CL

_{int, in vivo}. The results showed a good agreement with observed in vivo clearance. Although a CL

_{int, in vitro}obtained from dexamethasone-treated microsomes provided an accurate estimate of 77% of the observed CL

_{int, in vivo}, the limitation similar to that of Houston [60] persisted. The relationship between CL

_{int, in vitro}and CL

_{int, in vivo}was investigated empirically rather than mechanistically. Nonetheless, this study suggested that variation in CYP content affects the prediction of in vivo clearance. It provides evidence supporting the incorporation of CYP content as a covariate affecting the IIV in the IVIVE model.

_{u,mic}factor by Howgate et al. [65]. Underestimation of the parameter is a general issue in the IVIVE method. Inclusion of the microsomal protein content and CYP abundances that affect the IIV did not show the trend of underestimation.

#### Microsomal Protein per Gram of Liver (MPPGL)

_{int, in vitro}to CL

_{int, in vivo}using liver microsomes data or the rhCYP system as shown in Figure 2. It is a value with varying degrees of IIV. However, investigators have been using fixed values either due to the lack of information or empirically.

#### Inter-System Extrapolation Factor (ISEF)

_{int, in vitro}to correct a flaw in the original RAF, which was calculated with V

_{max}alone while the K

_{m}value was ignored. In their study, RAF represents the ratio of CL used to predict clearance of azelastine. It best reflects observed N-demethylation CL in HLM.

#### 3.1.4. Additional Correction Factors

#### F_{I}

_{H}based on differences in intra- and extra-cellular pH of the unbound drug fraction using F

_{I}as presented in Equations (57) to (60). These equations yielded higher values (up to 6.3-fold) of CL

_{H}for a basic compound (F

_{I}> 1) for strong diprotic bases, but lower values (up to 6.3-fold) of CL

_{H}for an acidic compound (F

_{I}< 1) for strong diprotic acids. The author suggests that the modified equation with F

_{I}improved the issue of both under- and over-estimation commonly encountered in IVIVE. Therefore, for basic compounds, the modified equation could improve the prediction of CL

_{H}. For acidic drugs, the conventional IVIVE equation tends to overestimate the CL

_{H}. However, this modified equation also improves the prediction of CL

_{H}for acidic compounds. Especially, the ionization factor significantly influences the calculation of CL

_{H}for drugs with a low extraction ratio since CL

_{H}is directly proportional to F

_{I}in this case.

#### Effective Fraction Unbound in Plasma

_{int}and high binding affinity for proteins commonly encountered when predicting human CL from in vitro data. Equations suggested by Poulin presented in Equations (61) to (62), incorporate the new correction factor of unbound fraction in the liver.

#### 3.1.5. Physiologically-Based IVIVE Model

_{inf}and fn

_{H}; and PS

_{inf,pas}and fn

_{met}. In vitro data (i.e., hepatic uptake data) based on suspensions of human hepatocytes fn

_{H}and fn

_{met}can be calculated using the equations.

## 4. Application of AS for the Prediction of Human PK Parameters

#### 4.1. Concept of AS

_{max}), 1 for volume of organs and blood flows, and 0.25 for physiological times [18,88]. AS assumes that mammals share similar anatomical, biochemical, and physiological features [16,21].

#### 4.2. Prediction of Clearance by AS

#### 4.2.1. Two-Term Method

#### 4.2.2. Rule of Exponent

#### 4.2.3. One or Two Species Method

#### 4.2.4. Liver Blood Flow

#### 4.2.5. Incorporation of in Vitro Data

#### 4.2.6. Protein Binding

_{u}= CL/f

_{u}) based on protein binding, in practice, f

_{u}does not significantly improve its predictability [22], [113].

_{u}and found that for drugs excreted renally or via extensive metabolism, CL

_{u}could not be predicted any better than total CL.

#### 4.2.7. QSAR Approach

#### 4.2.8. Fraction Unbound Intercept Correction Method (FCIM)

_{p}between rats and human (Rf

_{u}) are considered. The authors concluded that the new method significantly improved the prediction, even better than ROE. Furthermore, this method improved the prediction of vertical allometry.

#### 4.2.9. Multiexponential Allometric Scaling (MA)

#### 4.3. Prediction of Volume of Distribution by AS

#### 4.3.1. Volume of Distribution in PKs

_{d}) and generally estimated in PKs.

- Volume of distribution of central compartment (V
_{c}). - Volume of distribution at steady state (V
_{ss}) - Volume of distribution by area (V
_{area}), also known as V_{β}

_{c}is used as a correlation factor for the concentration and number of drugs in the body by the following equation:

_{c}is generally predicted from animal data. Its predictability is better than the others [114].

_{d}is clearly different from the actual tissue volume where drugs are distributed in the body:

_{bl}is the volume of blood, V

_{i}is the volume of organ, C

_{i}is the concentration in the organ, and K

_{i}is the partition coefficient (K

_{i}= C

_{i}/C). In this equation, the greater the tendency to distribute to tissues from blood (i.e., the greater K

_{i}), the greater is the V

_{d}.

#### 4.3.2. Prediction of V_{d}

_{d}, and the equations are presented in Table 4. In general, V

_{d}is well correlated with body weight, indicating that the exponent of V

_{d}is around 1 (usually between 0.8 and 1.1) [115]. Furthermore, for the prediction of V

_{d}, the two species in AS are acceptable compared to the use of three or more species. In the study of Mahmood and Balian [108], the average exponents using the simple AS for the prediction of V

_{d}are 0.89 and 0.90 in case of 3 and 2 species, respectively.

_{d}by AS has been investigated. As mentioned above, it is well known that protein binding properties vary between species. Furthermore, only unbound drugs penetrate blood vessels and biological membranes. For a drug with low binding affinity to plasma and tissue protein or drugs that are only distributed in the extracellular space, they can be scaled since total body water and extracellular water shows inverse correlation with animal size in AS [116].

_{d}may increase the accuracy of prediction results than the volume against unbound fraction in the plasma. In another study of Sawada et al. [118], the authors investigated the prediction of disposition of beta-lactam antibiotics and reported large differences in free volume of distribution between species. However, additional work revealed no advantage in consideration of the unbound fraction when Sawada et al.’s work was re-evaluated by adding six more drugs from the study of Mahmood [115].

#### 4.3.3. Prediction of Elimination Half-Life by AS

_{1/2}) is one of the most important PK parameter determining the dosage regimen and drugability. Predicted CL cannot estimate the t

_{1/2}since the V

_{d}and CL are required for the estimation of t

_{1/2}as presented by the equation:

_{1/2}, this parameter has been poorly estimated by AS [89,114]. Instead of direct scaling of t

_{1/2}, Mahmood [89] has suggested the calculation of t

_{1/2}as a secondary parameter using Equation (98). Another approach for prediction of human t

_{1/2}is based on the mean residence time (MRT) [114]. The MRT represents the average staying time of the drug in a body organ or compartment as the molecules diffuses in and out [28] and the parameter is estimated by the following equation:

_{ss}is the summation of the volume of the central compartment (V

_{c}) and peripheral compartment (V

_{p}) in a two-compartment PK model, MRT can also be expressed with the equation below combined with Equation (2) [28]:

_{1/2}was predicted using the predicted MRT by following equation:

## 5. Prediction of Absorption Related PK Parameters

_{a}) is generally expressed by first or zero order constant. It could be estimated from various PK models. However, k

_{a}is originally an apparent parameter that can be best estimated through first-order loss of drug from the gastrointestinal tract, not through first-order appearance of drug in the plasma [52].

_{m}) in Michaelis-Menten equation applied by body weight scaling. [88]. Although AS equation for scaling the first order kinetic parameter (i.e., k) has been suggested by Kenyon [88] as shown in Equation (102) in Table 5, further evaluation is required.

_{eff}) with physicochemical properties or Caco2 in vitro data have been reported. They are shown in Table 5. The k

_{a}was estimated with the predicted P

_{eff}combined with Equation (112). Another way to predict k

_{a}is to use the mean value of absorption parameters from animal data. Liu et al. [123] have reported a method for human PK projection of imigliptin using IVIVE, AS, and PK/PD modeling. In their study, the absorption parameter was applied as the mean value in non-clinical animal models such as rats, dogs, and monkeys.

_{a}) have been reported by a few investigators. In Equation (115), F

_{a}is predicted by a mechanism-based model using equilibrium solution for k

_{a}. Other relationships between F

_{a}and P

_{eff}are presented in Equation (116). The empirical equation could be used for prediction of F

_{a}using in vitro permeability data.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADME | absorption, distribution, metabolism, excretion |

AS | allometric scaling |

AUC_{0-inf} | area under the concentration-time curve from zero to infinity |

BDDCS | biopharmaceutics drug disposition classification system |

BW | brain weight |

CB | drug concentration in blood |

CL | clearance |

CLH | hepatic clearance |

CL_{int} | intrinsic clearance |

CL_{int, H} | hepatic intrinsic clearance |

CL_{int,H, human} | human hepatic intrinsic clearance |

CL_{int,H, pred} | predicted hepatic intrinsic clearance |

CL_{int,in vitro} | in vitro intrinsic clearance |

CL_{int,met} | intrinsic metabolic clearance |

CL_{int,sec} | intrinsic secretory clearance |

CL_{met} | metabolic clearance |

cLogP | partition coefficient |

clogP | calculated logP |

CL_{org} | organ clearance |

C_{P} | drug concentration in plasma |

C_{R} | concentration in VR |

C_{RBC} | drug concentration in red blood cells |

C_{u} | unbound drug concentration at distribution equilibrium |

DMPK | drug metabolism and pharmacokinetic |

D_{N} | dispersion number |

ECM | extended clearance model |

ER | extraction ratio |

ER_{H} | hepatic extraction ratio |

ER_{H, obs} | observed hepatic extraction ratio |

ER_{H, pred} | predicted hepatic extraction ratio |

F | fraction of absorption |

${\mathrm{f}}_{\mathrm{IW}}^{\mathrm{i}}$ | unbound fraction in the intracellular water of ionized compound |

${\mathrm{f}}_{\mathrm{IW}}^{\mathrm{n}}$ | unbound fraction in the intracellular water of neutral compound |

${\mathrm{f}}_{\mathrm{p}}^{\mathrm{i}}$ | unbound fraction in the plasma of ionized compound |

${\mathrm{f}}_{\mathrm{p}}^{\mathrm{n}}$ | unbound fraction in the plasma of neutral compound |

F_{a} | fraction of absorption |

f_{b} | unbound fraction in blood |

FCIM | fraction unbound intercept correction method |

F_{H} | hepatic availability |

F_{I} | ionization factor |

f_{nH} | fractional contribution of hepatic elimination |

f_{nmet} | fractional contribution of metabolic elimination |

f_{nsec} | fractional contribution of biliary elimination |

f_{p} | unbound fraction in plasma |

F_{PO} | oral bioavailability |

f_{u, mic} | non-specific binding factor to microsomes |

f_{u,liver} | unbound fraction into the liver |

Ha | number of hydrogen-bond acceptors |

HBD | number of hydrogen-bond donor |

Hct | hematocrit |

HLM | human liver microsomes |

IIV | inter-individual variability |

ISEF | inter-system extrapolation factor |

ISTD | internal standard |

IVIVE | in vitro-in vivo extrapolation |

IW | intracellular water |

k_{a} | absorption rate constant |

k_{a,eq} | equilibrium solution for k_{a} |

k_{i} | the rate constant of intestinal transit |

K_{m} | Michaelis constant |

L | length of perfusion segment |

MA | multiexponential allometric scaling |

MLBF | monkey liver blood flow |

MLP | maximum life-span potential |

MPPGL | microsomal protein per gram of liver |

MPR | microsomal protein recovery |

MRT | mean residence time |

MW | molecular weight |

NCA | non-compartmental analysis |

P_{eff} | effective permeability |

PK | pharmacokinetic |

PLR | plasma to whole liver concentration ratio |

P_{m} | drug permeability across intestinal mucosa |

PSA | polar surface area |

PS_{bile} | biliary clearance |

PS_{efflux, total} | apparent sinusoidal total efflux clearance from the intracellular side of hepatocytes back into blood |

PS_{inf, act} | sinusoidal efflux from hepatocytes back into blood |

PS_{uptake,total} | total apparent uptake clearance |

Q_{H} | hepatic liver flow |

QSAR | quantitative structure activity relationship |

R | radius of human jejunum |

RAF | relative activity factor |

R_{B/P} | blood to plasma ratio |

R_{E/I} | ratio of distributed albumin in the extravascular space to that in the intravascular space |

R_{fu} | unbound fraction in plasma ratio between rats and humans |

rhCYP | recombinant human CYP system |

R_{N} | efficiency number |

ROE | rule of exponent |

S | absorptive surface area |

t_{1/2} | half-life |

V | volume of distribution |

V_{area}, V_{β} | volume of distribution by area |

V_{c} | volume of distribution of central compartment |

V_{E} | extracellular space volume minus the plasma volume |

V_{max} | maximal rate of the reaction |

V_{met} | metabolic rate |

V_{plasma} | plasma volume |

V_{R} | physical volume into which the drug distributes minus the extracellular space |

V_{ss} | volume of distribution at steady state |

W | body weight |

ε^{2} | variance for each sinusoid in the whole liver |

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**Figure 1.**The perfusion model including one reservoir and one clearing organ. In this model, Q refers to the rate of perfusate or blood flow. C

_{in}is the drug concentration in the artery entering the reservoir and clearing organ. C

_{out}denotes the drug concentration in veins leaving the clearing organ and entering the reservoir, which is a non-clearing organ. V

_{E}and V

_{R}indicate the volume of clearing organ and reservoir, respectively. The elimination process is followed by first-order kinetics and its elimination constant is represented by k

_{el}. C

_{E}is the drug concentration in the clearing organ.

**Figure 2.**The scheme of the overall in vitro-in vivo extrapolation (IVIVE) process using human liver microsomes or recombinant human cytochrome P450 (CYP) system. MPPGL refers to the microsomal protein per gram of liver.

Model | Scheme ^{1} | CL_{H} ^{2} | ER_{H} |
---|---|---|---|

Well-stirred | $\frac{{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}\xb7{\mathrm{f}}_{\mathrm{p}}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}\xb7{\mathrm{f}}_{\mathrm{p}}}$ | $\frac{{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}\xb7{\mathrm{f}}_{\mathrm{p}}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}\xb7{\mathrm{f}}_{\mathrm{p}}}$ | |

Parallel tube | ${\mathrm{Q}}_{\mathrm{H}}\xb7{\displaystyle \left\{1-{\mathrm{e}}^{-\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}\right)}\right\}}$ | $1-{\mathrm{e}}^{-\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}\right)}$ | |

Distributed | ${\mathrm{Q}}_{\mathrm{H}}\xb7{\displaystyle \left\{1-{\mathrm{e}}^{-\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}+\frac{1}{2}\xb7{\mathsf{\epsilon}}^{2}{\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}\right)}^{2}\right)}\right\}}$ | $1-{\mathrm{e}}^{-\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}+\frac{1}{2}\xb7{\mathsf{\epsilon}}^{2}{\left(\frac{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{H}}}{{\mathrm{Q}}_{\mathrm{H}}}\right)}^{2}\right)}$ | |

Dispersion | ${\mathrm{Q}}_{\mathrm{H}}\xb7{\displaystyle \left\{1-\frac{4\mathrm{a}}{{\left(1+\mathrm{a}\right)}^{2}\xb7{\mathrm{e}}^{\left[\frac{\mathrm{a}-1}{2{\mathrm{D}}_{\mathrm{N}}}\right]}-{\left(1-\mathrm{a}\right)}^{2}\xb7{\mathrm{e}}^{-\left[\frac{\mathrm{a}+1}{2{\mathrm{D}}_{\mathrm{N}}}\right]}}\right\}}$ | $1-\frac{4\mathrm{a}}{{\left(1+\mathrm{a}\right)}^{2}\xb7{\mathrm{e}}^{\left[\frac{\mathrm{a}-1}{2{\mathrm{D}}_{\mathrm{N}}}\right]}-{\left(1-\mathrm{a}\right)}^{2}\xb7{\mathrm{e}}^{-\left[\frac{\mathrm{a}+1}{2{\mathrm{D}}_{\mathrm{N}}}\right]}}$ |

^{1}Dotted line indicates the concentration–distance profile within liver.

^{2}Where Q

_{H}is hepatic liver flow expressed as a unit of mL/min/kg.

**Table 2.**Mathematical equations of the IVIVE approach for prediction of clearance from in vitro data.

Equation | Comment * | Ref. | |
---|---|---|---|

${\mathrm{CL}}_{\mathrm{int},invitro}=\frac{{\mathrm{V}}_{\mathrm{max}}}{{\mathrm{K}}_{\mathrm{m}}}=\frac{\mathrm{rate}\mathrm{of}\mathrm{metabolism}}{{\mathrm{C}}_{\mathrm{E}}}$ | (38) | Basic principle of IVIVE was suggested Provide the 4 stages for the IVIVE | [60] |

${\mathrm{CL}}_{\mathrm{H},invivo}=\frac{{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{f}}_{\mathrm{b}}\xb7{\mathrm{CL}}_{\mathrm{int},invivo}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{f}}_{\mathrm{b}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{in}\mathrm{vivo}}}{\mathrm{or}\mathrm{CL}}_{\mathrm{int}}=\frac{{\mathrm{CL}}_{\mathrm{H}}}{{\mathrm{f}}_{\mathrm{b}}\left(1-\mathrm{E}\right)}$ | (39) | ||

${\mathrm{CL}}_{\mathrm{int}.invitro}=\frac{\mathrm{Initial}\mathrm{amount}\mathrm{in}\mathrm{the}\mathrm{incubation}}{{\mathrm{AUC}}_{invitro}}$ | (40) | Empirically the scaling factor (SF) was estimated as the value of 8.9 Predicted ER _{H} and observed ER_{H} are ER_{H, pred} and ER_{H, obs}, respectively Provide criteria for the classification of the drugs into: low extraction, ER _{H} < 0.3; intermediate, 0.3 < ER_{H} < 0.7; high extraction, ER_{H} > 0.7 | [61] |

${\mathrm{ER}}_{\mathrm{H},\mathrm{pred}}=\frac{\mathrm{SF}\xb7{\mathrm{CL}}_{\mathrm{int},invitro}}{{\mathrm{Q}}_{\mathrm{H}}+\left(\mathrm{SF}\xb7{\mathrm{CL}}_{\mathrm{int},invitro}\right)}$ | (41) | ||

${\mathrm{ER}}_{\mathrm{H},\mathrm{obs}}=\frac{\mathrm{CL}}{{\mathrm{Q}}_{\mathrm{H}}}$ | (42) | ||

${\mathrm{CL}}_{\mathrm{int},\mathrm{H},\mathrm{human}}=\frac{0.693}{invitro{\mathrm{t}}_{1/2}}\xb7\frac{\mathrm{mL}\mathrm{incubation}}{\mathrm{mg}\mathrm{microsomes}}\xb7\frac{45\mathrm{mg}\mathrm{microsomes}}{\mathrm{g}\mathrm{liver}}\xb7\frac{20\mathrm{mg}\mathrm{liver}}{\mathrm{kg}\mathrm{body}\mathrm{weight}}$ | (43) | Investigation of the effect of the protein binding into the plasma and microsomes The ISTD refers to the internal standard | [62] |

${\mathrm{f}}_{\mathrm{u},\mathrm{mic}}=\frac{\raisebox{1ex}{$\mathrm{drug}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{ISTD}$}\right.\mathrm{peak}\mathrm{height}\mathrm{ratio}\mathrm{in}\mathrm{buffer}\mathrm{sample}}{2\xb7\raisebox{1ex}{$\mathrm{drug}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{ISTD}$}\right.\mathrm{peak}\mathrm{height}\mathrm{ratio}\mathrm{in}\mathrm{microsome}\mathrm{sample}}$ | (44) | ||

${\mathrm{CL}}_{\mathrm{int},\mathrm{H},\mathrm{pred}.}={\mathrm{CL}}_{\mathrm{int},invitro}\xb7\mathrm{animal}\mathrm{scaling}\mathrm{factor}$ | (45) | Animal scaling factor was incorporated into IVIVE | [66] |

$\mathrm{Animal}\mathrm{Scaling}\mathrm{factor}=\frac{{\mathrm{CL}}_{\mathrm{int},\mathrm{H},invivo}}{{\mathrm{CL}}_{\mathrm{int},invitro}}$ | (46) | ||

${\mathrm{f}}_{\mathrm{u},\mathrm{mic}}=\frac{\mathrm{unchanged}\mathrm{compound}\mathrm{concentration}\mathrm{in}\mathrm{buffer}}{\mathrm{unchanged}\mathrm{compound}\mathrm{concentration}\mathrm{in}\mathrm{microsome}}$ | (47) | ||

${\mathrm{CL}}_{\mathrm{int},invivo,\mathrm{pred}}={\mathrm{CL}}_{\mathrm{int},invitro}\xb7\mathrm{MPR}=\frac{{\mathrm{V}}_{\mathrm{max}}}{{\mathrm{K}}_{\mathrm{M}}}\xb7\mathrm{MPR}$ | (48) | Microsomal protein recovery (MPR) ratio was incorporated in IVIVE R _{B/P} refers to blood to plasma ratio | [67] |

$\mathrm{MPR}\left(\mathrm{mg}\mathrm{protein}/\mathrm{g}\mathrm{liver}\right)=\frac{\mathrm{Liver}\mathrm{homogenate}\mathrm{CYP}\mathrm{content}\left(\mathrm{nmol}/\mathrm{g}\mathrm{liver}\right)}{\mathrm{Microsomal}\mathrm{CYP}\mathrm{content}\left(\mathrm{nmol}/\mathrm{mg}\mathrm{protein}\right)}$ | (49) | ||

${\mathrm{CL}}_{\mathrm{int}.invivo,\mathrm{obs}}=\frac{\mathrm{CL}}{{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{R}}_{\mathrm{B}/\mathrm{P}}}$ | (50) | ||

$\mathrm{P}450\mathrm{content}\mathrm{correcting}\mathrm{factor}=\frac{\mathrm{P}450\mathrm{isozyme}\mathrm{content}/\mathrm{g}\mathrm{liver}}{\mathrm{P}450\mathrm{isozyme}\mathrm{content}/\mathrm{mg}\mathrm{protein}}$ | (51) | CYP abundance was incorporated in IVIVE | [68] |

$\mathrm{RAF}=\frac{{\mathrm{V}}_{\mathrm{max}}\left(\mathrm{HML}\right)}{{\mathrm{V}}_{\mathrm{max}}\left(\mathrm{rhCYP}\right)}$ | (52) | Relative activity factor (RAF) introduced for scaling rhCYP data to HLM Modified RAF taking into account of K _{m} | [69,70] |

$\mathrm{RAF}=\frac{{\mathrm{CL}}_{\mathrm{int}}\left(\mathrm{HML}\right)}{{\mathrm{CL}}_{\mathrm{int}}\left(\mathrm{rhCYP}\right)}$ | (53) | ||

${\mathrm{CL}}_{\mathrm{int}}=[{\displaystyle {\displaystyle \sum}_{\mathrm{j}=1}^{\mathrm{n}}}{\displaystyle \left({\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\frac{{\mathrm{V}}_{\mathrm{max}}{\left({\mathrm{rhCYP}}_{\mathrm{j}}\right)}_{\mathrm{i}}\times {\mathrm{RAF}}_{\mathrm{ij}}\left({\mathrm{V}}_{\mathrm{max}}\right)}{{\mathrm{K}}_{\mathrm{m}}{\left({\mathrm{rhCYP}}_{\mathrm{j}}\right)}_{\mathrm{i}}}\right)}]\times \mathrm{MPPGL}\times \mathrm{Liver}\mathrm{weight}$ | (54) | ||

$\mathrm{ISEF}=\frac{{\mathrm{V}}_{{\mathrm{max}}_{\mathrm{ji}}}\left(\mathrm{HML}\right)}{{\mathrm{V}}_{{\mathrm{max}}_{\mathrm{i}}}\left({\mathrm{rhCYP}}_{\mathrm{j}}\right)\times {\mathrm{CYP}}_{\mathrm{j}}\mathrm{abundance}\left(\mathrm{HLM}\right)}$ | (55) | Inter-system extrapolation factor (ISEF) is introduced for scaling rhCYP data to HLM | [69] |

${\mathrm{CL}}_{\mathrm{int}}=[{\displaystyle {\displaystyle \sum}_{\mathrm{j}=1}^{\mathrm{n}}}\left({\displaystyle {\displaystyle \sum}_{\mathrm{i}-1}^{\mathrm{n}}}\frac{{\mathrm{V}}_{{\mathrm{max}}_{\mathrm{i}}}\left({\mathrm{rhCYP}}_{\mathrm{j}}\right)\times {\mathrm{CYP}}_{\mathrm{j}}\mathrm{abundance}}{{\mathrm{K}}_{\mathrm{m}}{\left({\mathrm{rhCYP}}_{\mathrm{j}}\right)}_{\mathrm{i}}}\right)]\times \mathrm{MPPGL}\times \mathrm{Liver}\mathrm{weight}$ | (56) | ||

${\mathrm{CL}}_{\mathrm{H}}=\frac{{\mathrm{R}}_{\mathrm{B}/\mathrm{P}}\xb7{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},\mathrm{human}}\xb7{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{F}}_{\mathrm{I}}}{{\mathrm{R}}_{\mathrm{B}/\mathrm{P}}\xb7{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},\mathrm{human}}\xb7{\mathrm{f}}_{\mathrm{p}}\xb7{\mathrm{F}}_{\mathrm{I}}}$ | (57) | The ionization factor is incorporated into the IVIVE F _{I} is an ionization factor Subscript letter IW denotes intracellular water Upper letter i and n indicate compounds of ionized and neutral forms, respectively | [71] |

${\mathrm{F}}_{\mathrm{I}}=\frac{{\mathrm{f}}_{\mathrm{p}}^{\mathrm{n}}}{{\mathrm{f}}_{\mathrm{IW}}^{\mathrm{n}}}=\frac{1-{\mathrm{f}}_{\mathrm{p}}^{\mathrm{i}}}{1-{\mathrm{f}}_{\mathrm{IW}}^{\mathrm{i}}}$ | (58) | ||

${\mathrm{f}}_{\mathrm{acid}}^{\mathrm{i}}=\frac{\left[{\mathrm{A}}^{-}\right]}{{\left[\mathrm{AH}\right]}_{0}}=\frac{1}{1+{10}^{\mathrm{p}{K}_{\mathrm{a}}-\mathrm{pH}}}$ | (59) | ||

${\mathrm{f}}_{\mathrm{base}}^{\mathrm{i}}=\frac{\left[{\mathrm{BH}}^{+}\right]}{{\left[\mathrm{B}\right]}_{0}}=\frac{1}{1+{10}^{\mathrm{pH}-\mathrm{p}{K}_{\mathrm{a}}}}$ | (60) | ||

${\mathrm{CL}}_{\mathrm{H}}=\frac{{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},\mathrm{human}}\xb7{\mathrm{f}}_{\mathrm{u},\mathrm{liver}}/{\mathrm{f}}_{\mathrm{u},\mathrm{mic}}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},\mathrm{human}}\xb7{\mathrm{f}}_{\mathrm{u},\mathrm{liver}}/{\mathrm{f}}_{\mathrm{u},\mathrm{mic}}}$ | (61) | The unbound fraction into the liver (f_{u,liver}) is incorporated into the IVIVE Plasma to whole liver concentration ratio (PLR) = 13.3 | [72] |

${\mathrm{f}}_{\mathrm{u},\mathrm{liver}}=\frac{\mathrm{PLR}\xb7{\mathrm{f}}_{\mathrm{u},\mathrm{p},\mathrm{app}}}{1+\left(\mathrm{PLR}-1\right)\xb7{\mathrm{f}}_{\mathrm{u},\mathrm{p},\mathrm{app}}}$ | (62) | ||

${\mathrm{CL}}_{\mathrm{int},\mathrm{liver},invitro}={\mathrm{PS}}_{\mathrm{uptake},\mathrm{total}}\xb7\frac{{\mathrm{CL}}_{\mathrm{met}}+{\mathrm{PS}}_{\mathrm{bile}}}{{\mathrm{CL}}_{\mathrm{met}}+{\mathrm{PS}}_{\mathrm{efflux},\mathrm{total}}+{\mathrm{PS}}_{\mathrm{bile}}}$ | (63) | Physiologically-based IVIVE model Total apparent uptake clearance (PS _{uptake,total}) consists of saturable and/or non-saturable processes CL _{met} and PS_{bile} refer to metabolic and biliary clearance, respectively Apparent sinusoidal total efflux clearance from the intracellular side of hepatocytes back into blood (PS _{efflux, total}) consists of saturable and/or non-saturable processes | [73] |

${\mathrm{CL}}_{\mathrm{H}}=\frac{{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},invitro}\xb7{\mathrm{f}}_{\mathrm{p}}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{liver},invitro}\xb7{\mathrm{f}}_{\mathrm{p}}}$ | (64) | ||

${\mathrm{fn}}_{\mathrm{H}}={\mathrm{fn}}_{\mathrm{sec}}+{\mathrm{fn}}_{\mathrm{met}}$ | (65) | Provide the method for the prediction of total clearance and relative elimination contributions The fn _{H,} fn_{sec,} and fn_{met} refers to a fractional contribution of hepatic, biliary, and metabolic elimination to overall clearance PS _{inf, act} and PS_{inf, pas} refer to the sinusoidal active and passive influx clearance, respectively Sinusoidal efflux from hepatocytes back into blood (PS _{eff}) is assumed to occur via passive diffusion, therefore PS_{eff} = PS_{inf,pas} CL _{int,sec} and CL_{int,met} refer to intrinsic secretory and metabolic clearance, respectively PS _{inf} equals to the sum of PS_{inf,act} and PS_{inf,pas} which are determined by suspension of pooled human hepatocytes (unit: mL/min/kg) | [8] |

${\mathrm{fn}}_{\mathrm{H}}=1-{\mathrm{e}}^{-0.01741{\mathrm{PS}}_{\mathrm{inf}}}$ | (66) | ||

${\mathrm{fn}}_{\mathrm{met}}=1-{\mathrm{e}}^{-0.01521{\mathrm{PS}}_{\mathrm{inf},\mathrm{pas}}}$ | (67) | ||

${\mathrm{CL}}_{\mathrm{renal}}={\mathrm{CL}}_{\mathrm{total}}-{\mathrm{CL}}_{\mathrm{H}}$ | (68) | ||

${\mathrm{CL}}_{\mathrm{total}}=\frac{{\mathrm{CL}}_{\mathrm{H}}}{{\mathrm{fn}}_{\mathrm{H}}}$ | (69) | ||

${\mathrm{CL}}_{\mathrm{int},invitro}=\frac{\left({\mathrm{PS}}_{\mathrm{inf},\mathrm{act}}+{\mathrm{PS}}_{\mathrm{inf},\mathrm{pas}}\right)\xb7\left({\mathrm{CL}}_{\mathrm{int},\mathrm{sec}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{met}}\right)}{{\mathrm{PS}}_{\mathrm{eff},\mathrm{total}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{sec}}+{\mathrm{CL}}_{\mathrm{int},\mathrm{met}}}$ | (70) | ||

${\mathrm{CL}}_{\mathrm{H}}=\frac{{\mathrm{Q}}_{\mathrm{H}}\xb7{\mathrm{CL}}_{\mathrm{int},invitro}\xb7{\mathrm{f}}_{\mathrm{p}}}{{\mathrm{Q}}_{\mathrm{H}}+{\mathrm{CL}}_{\mathrm{int},invitro}\xb7{\mathrm{f}}_{\mathrm{p}}}$ | (71) |

Method | Equation | Comments * | Ref. | |
---|---|---|---|---|

Simple AS | $\mathrm{CL}=\mathrm{a}{\left(\mathrm{W}\right)}^{\mathrm{b}}$ | (74) | Select a proper equation by the rule of exponent (ROE) W and BW represent body and brain weight, respectively | - |

AS with MLP ^{1} | $\mathrm{CL}\xb7\mathrm{MLP}=\mathrm{a}{\left(\mathrm{W}\right)}^{\mathrm{b}}$ | (75) | - | |

AS with BW | $\mathrm{CL}\xb7\mathrm{BW}=\mathrm{a}{\left(\mathrm{W}\right)}^{\mathrm{b}}$ | (76) | [89] | |

Rule of exponent | If the exponent is 0.55 to 0.7, then use the simple AS, Equation (74) | [90] | ||

If the exponent is 0.71 to 1, then use the MLP, Equation (75) | ||||

If the exponent is more than 1, then use the BW, Equation (76) | ||||

Two-term method | $\mathrm{CL}=\mathsf{\theta}{\left(\mathrm{W}\right)}^{\mathrm{a}}\xb7{\left(\mathrm{BW}\right)}^{\mathrm{b}}$ | (77) | θ is a constant, which is determined by multiple regression analysis | [91] |

Multiexponential | ${\mathrm{CL}}_{\mathrm{human}}={\mathrm{aW}}^{\mathrm{b}}+\left[\left(\frac{1-\frac{3}{2}\mathrm{b}}{1-\frac{1}{2}\mathrm{b}}\right)\right]{\mathrm{aW}}^{0.9}$ | (78) | The unit of CL is mL/min | [92] |

Normalized AS | ${\mathrm{CL}}_{\mathrm{animal}}\frac{{\mathrm{CL}}_{\mathrm{int},\mathrm{human}}}{{\mathrm{CL}}_{\mathrm{int},\mathrm{animal}}}=\mathrm{a}{\left(\mathrm{W}\right)}^{\mathrm{b}}$ | (79) | CL_{int} refers the unbound CL_{int} in microsomes or hepatocytes in species and humans | [93] |

One species AS | ${\mathrm{CL}}_{\mathrm{human}}={\mathrm{CL}}_{\mathrm{animal}}\xb7{\left(\frac{{\mathrm{W}}_{\mathrm{human}}}{{\mathrm{W}}_{\mathrm{animal}}}\right)}^{\mathrm{b}}$ | (80) | The exponent b is a constant 0.75, which is physiologically relevant value (e.g., blood flow, filtration, etc.) | [94,95] |

One species AS | ${\mathrm{CL}}_{\mathrm{pred}}=0.152\xb7{\mathrm{CL}}_{\mathrm{rat}}\xb7\left(\frac{{\mathrm{W}}_{\mathrm{human}}}{{\mathrm{W}}_{\mathrm{rat}}}\right)$ | (81) | Predict the CL of bound drug | [90] |

${\mathrm{CL}}_{\mathrm{pred}}=0.41\xb7{\mathrm{CL}}_{\mathrm{dog}}\xb7\left(\frac{{\mathrm{W}}_{\mathrm{human}}}{{\mathrm{W}}_{\mathrm{dog}}}\right)$ | (82) | |||

${\mathrm{CL}}_{\mathrm{pred}}=0.407\xb7{\mathrm{CL}}_{\mathrm{monkey}}\xb7\left(\frac{{\mathrm{W}}_{\mathrm{human}}}{{\mathrm{W}}_{\mathrm{monkey}}}\right)$ | (83) | |||

Two species AS | ${\mathrm{CL}}_{\mathrm{pred}}={\mathrm{a}}_{\mathrm{rat}-\mathrm{dog}}\xb7{\mathrm{W}}_{\mathrm{human}}{}^{0.628}$ | (84) | Predict the CL of bound drug | |

${\mathrm{CL}}_{\mathrm{pred}}={\mathrm{a}}_{\mathrm{rat}-\mathrm{monkey}}\xb7{\mathrm{W}}_{\mathrm{human}}{}^{0.650}$ | (85) | |||

Hepatic liver method | ${\mathrm{CL}}_{\mathrm{pred}}={\mathrm{CL}}_{\mathrm{animal}}\xb7\left(\frac{{\mathrm{Q}}_{\mathrm{H},\mathrm{human}}}{{\mathrm{Q}}_{\mathrm{H},\mathrm{animal}}}\right)$ | (86) | [96] | |

FCIM ^{2} | $\mathrm{CL}=33.35\times {\left(\frac{\mathrm{a}}{{\mathrm{Rf}}_{\mathrm{u}}}\right)}^{0.77}$ | (87) | Rf_{u} is the f_{u} ratio between rats and humans and a is the coefficient form AS The unit of CL is mL/min | [97] |

QSAR ^{3} | $\begin{array}{ll}{\mathrm{LogCL}}_{\mathrm{pred}}& =0.433\xb7\mathrm{log}({\mathrm{CL}}_{\mathrm{rat}})\\ & +1.0\xb7\mathrm{log}({\mathrm{CL}}_{\mathrm{dog}})\\ & -0.00627\xb7\mathrm{MW}+0.189\xb7\mathrm{Ha}\\ & -0.00111\xb7\mathrm{log}({\mathrm{CL}}_{\mathrm{dog}})\xb7\mathrm{MW}\\ & +0.0000144\xb7{\mathrm{MW}}^{2}\\ & -0.0004\xb7\mathrm{MW}\xb7\mathrm{Ha}-0.707\end{array}$ | (88) | The unit of observed and predicted CL value is mL/min/kg | [98] |

$\begin{array}{l}{\mathrm{LogCL}}_{\mathrm{po},\mathrm{pred}}\\ =-0.5927+0.7386\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{rat}}\right)\\ +0.5040\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\\ +0.06014\mathrm{clogP}\\ -0.1862\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\times \mathrm{clogP}\\ +0.02893\mathrm{MW}\times \mathrm{clogP}\\ +0.02893\mathrm{MW}\times \mathrm{clogP}\\ +0.02551\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{rat}}\right)\\ \times \mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{rat}}\right)\mathrm{clogP}\\ -0.03029\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{rat}}\right)\times \mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\\ \times \mathrm{Ha}\\ -0.03051\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{rat}}\right)\times \mathrm{MW}\times \mathrm{clogP}\\ +0.08461\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\times \mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\\ \times \mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\\ -0.2510\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\times \mathrm{log}({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}})\\ \times \mathrm{MW}\\ +0.06061\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\times \mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\\ \times \mathrm{Ha}\\ +0.04607\mathrm{log}\left({\mathrm{CL}}_{\mathrm{po},\mathrm{dog}}\right)\times \mathrm{clogP}\times \mathrm{clogP}\\ -0.003596\mathrm{clogP}\times \mathrm{clogP}\times \mathrm{Ha}\\ +0.0005963\mathrm{clogP}\times \mathrm{Ha}\times \mathrm{Ha}\end{array}$ | (89) | The unit of observed and predicted oral CL value is mL/min/kg | [99] |

^{1}The maximum life-span potential (MLP) is calculated by the equation MPL (years) = 185.4BW

^{0.636}W

^{−0.225}[100].

^{2}Fraction unbound intercept correction method.

^{3}Quantitative structure activity relationship (QSAR) consist of physicochemical properties, such as molecular weight (MW), partition coefficient (cLogP), and number of hydrogen-bound acceptors (Ha).

Method | Equation | Comment * | Ref. | |
---|---|---|---|---|

Simple AS | $\mathrm{V}=\mathrm{a}{\left(\mathrm{W}\right)}^{\mathrm{b}}$ | (93) | The prediction of V_{d} is well predicted equally with using two species in AS | [108] |

Average fraction unbound in tissue ^{1} | $\mathrm{V}={\mathrm{V}}_{\mathrm{Plasma}}\left(1+{\mathrm{R}}_{\mathrm{E}/\mathrm{I}}\right)+{\mathrm{f}}_{\mathrm{u}}\xb7{\mathrm{V}}_{\mathrm{P}}\left(\frac{{\mathrm{V}}_{\mathrm{E}}}{{\mathrm{V}}_{\mathrm{p}}}-\frac{{\mathrm{V}}_{\mathrm{R}}\xb7{\mathrm{f}}_{\mathrm{u}}}{{\mathsf{\alpha}}_{\mathrm{R}}}\right)$ | (94) | It is useful to analyze and predict an alteration in apparent V_{d} then identify the cause of alteration. It is particularly useful for drugs with low V _{d} (<15 L or 0.2 L/kg) | [119] |

Proportionality | ${\mathrm{V}}_{\mathrm{human},\mathrm{pred}}=\frac{{\mathrm{V}}_{\mathrm{animal}}\xb7{\mathrm{f}}_{\mathrm{u},\mathrm{human}}}{{\mathrm{f}}_{\mathrm{u},\mathrm{animal}}}$ | (95) | It is assumed that the volume of distribution at a steady state of free drug is identical between species | [120] |

One species AS | ${\mathrm{V}}_{\mathrm{human},\mathrm{pred}}=-0.35{\mathrm{V}}_{\mathrm{rat}}{}^{0.91}$ | (96) | Statistical modeling is applied in this model | [121] |

QSAR | $\begin{array}{ll}\mathrm{log}\left({\mathrm{Vd}}_{\mathrm{ss},\mathrm{human}}\right)& =0.1859\xb7\mathrm{log}\left({\mathrm{Vd}}_{\mathrm{ss},\mathrm{rat}}\right)\times \mathrm{log}\left({\mathrm{Vd}}_{\mathrm{ss},\mathrm{rat}}\right)\\ & -0.3887\xb7\mathrm{log}\left({\mathrm{Vd}}_{\mathrm{ss},\mathrm{rat}}\right)\times \mathrm{log}\left(\mathrm{MW}\right)\\ & +0.3089\xb7\mathrm{log}\left({\mathrm{Vd}}_{\mathrm{ss},\mathrm{dog}}\right)\times \mathrm{log}\left(\mathrm{MW}\right)\\ & +0.003306\xb7\mathrm{log}\left(\mathrm{MW}\right)\times \mathrm{c}\mathrm{log}\mathrm{P}\\ & +1.71\end{array}$ | (97) | Vd_{ss, human} (mL/kg) is predicted by QSAR modeling with quadratic term descriptors | [122] |

^{1}Where V

_{d}is apparent volume of distribution, V

_{plasma}is plasma volume, V

_{E}is extracellular space minus the plasma, V

_{R}is physical volume into which the drug distributes minus the extracellular space, f

_{u}is the fraction unbound in plasma, and R

_{E/I}is the ratio of distributed albumin in the extravascular space to that in the intravascular space. It is 1.4. α

_{R}equals to C

_{u}/C

_{R}where C

_{u}is unbound drug concentration at distribution equilibrium and C

_{R}is concentration in V

_{R}.

Method | Equation | Comments * | Ref. | |
---|---|---|---|---|

AS | ${\mathrm{k}}_{\mathrm{a}}={\mathrm{animal}\mathrm{k}}_{\mathrm{a}}\times {(\frac{{\mathrm{W}}_{\mathrm{human}}}{{\mathrm{W}}_{\mathrm{animal}}})}^{-0.25}$ | (102) | The unit of k_{a} is h in time^{−1} | [88] |

QSAR^{1} | ${\mathrm{logP}}_{\mathrm{eff}}=-2.883-0.01\mathrm{PSA}+0.192{\mathrm{logD}}_{5.5}-0.239\mathrm{HBD}$ | (103) | The choice of model for prediction depends on the availability of descriptor data Effective permeability in 10 ^{−4} cm/s | [124] |

${\mathrm{logP}}_{\mathrm{eff}}=-2.546-0.011\mathrm{PSA}-0.278\mathrm{HBD}$ | (104) | |||

${\mathrm{logP}}_{\mathrm{eff}}=-3.067+0.162\mathrm{clogP}-0.01\mathrm{PSA}-0.235\mathrm{HBD}$ | (105) | |||

Use of Caco2 data ^{2} | ${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.4926\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}-0.1454\left(\mathrm{at}\mathrm{pH}=7.4\right)$ | (106) | All tested drugs | [125] |

${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.6532\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}-0.3036\left(\mathrm{at}\mathrm{pH}=6.5\right)$ | (107) | |||

${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.6836\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}-0.5579\left(\mathrm{at}\mathrm{pH}=7.4\right)$ | (108) | Only passively diffused drugs | ||

${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.7254\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}-0.5441\left(\mathrm{at}\mathrm{pH}=6.5\right)$ | (109) | |||

${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.4898\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}+0.3311\left(\mathrm{at}\mathrm{pH}=7.4\right)$ | (110) | Only carrier-mediated drugs | ||

${\mathrm{P}}_{\mathrm{eff},\mathrm{human}}=0.542\mathrm{log}{\mathrm{P}}_{\mathrm{eff},\mathrm{Caco}2}+0.06\left(\mathrm{at}\mathrm{pH}=6.5\right)$ | (111) | |||

Sinko et al. ^{5} | ${\mathrm{k}}_{\mathrm{a}}=\frac{2{\mathrm{P}}_{\mathrm{eff}}}{\mathrm{R}}$ | (112) | The absorption rate constant is proportional to the P_{eff} | [126] |

Mechanism based modeling ^{3} | ${\mathrm{F}}_{\mathrm{a},\mathrm{pred}}=0.884{\mathrm{F}}_{\mathrm{a},\mathrm{exp}}+7.47$ | (113) | F_{a} is expressed as percent unit The equation is the result of the correlation between F _{a,pred} and F_{a,exp} | [127] |

${\mathrm{k}}_{\mathrm{a},\mathrm{eq}}=\frac{{\mathrm{P}}_{\mathrm{m}}\mathrm{S}}{{\mathrm{V}}_{\mathrm{c}}}$ | (114) | k_{a,eq} is expressed as the unit of min^{−1} k _{a,eq} is a key determinant for F_{a} and can be used as PK modeling | ||

${\mathrm{F}}_{\mathrm{a}}=\frac{{\mathrm{k}}_{\mathrm{a},\mathrm{eq}}}{{\mathrm{k}}_{\mathrm{i}}+{\mathrm{k}}_{\mathrm{a},\mathrm{eq}}}$ | (115) | |||

Compartmental absorption and transit model ^{4} | ${\mathrm{F}}_{\mathrm{a}}=1-{\left(1+0.54{\mathrm{P}}_{\mathrm{eff}}\right)}^{-7}$ | (116) | F_{a} is expressed as the fractional value. | [128] |

^{1}In this equation, passive intestinal absorption in humans was predicted. Abbreviations are: P

_{eff}, effective permeability; PSA, polar surface area; logD

_{5.5}, octanol/water distribution coefficient at pH 5.5; HBD, number of hydrogen bond donors; clogP, calculated logP value.

^{2, 5}P

_{eff}is calculated by the equation of P

_{eff}= Q(1-C

_{out}/C

_{in})/2πRL, where P

_{eff}is effective permeability, Q is perfusion rate (mL/min), C

_{out}and C

_{in}are outlet and inlet drug concentration, respectively, R is the radius of human jejunum (1.75 cm) [129], and L is the length of perfusion segment (10 cm). Caco2 permeability and human effective permeability are expressed with values of ×10

^{−6}cm/s and ×10

^{−4}cm/s, respectively.

^{3}k

_{a,eq}is the equilibrium solution for k

_{a}, P

_{m}is drug permeability across intestinal mucosa (×10

^{−6}cm/s), S is the absorptive surface area which is set at 200 m

^{2}, V

_{c}is the volume of distribution in well-perfused organs, k

_{i}is the rate constant of intestinal transit, which is set to be 5.025 × 10

^{−3}min

^{−1}as an inverse value of the average transit time [130] in human small intestine (approximately 199 min).

^{4, 5}P

_{eff}is human effective permeability in cm/h.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Choi, G.-W.; Lee, Y.-B.; Cho, H.-Y.
Interpretation of Non-Clinical Data for Prediction of Human Pharmacokinetic Parameters: In Vitro-In Vivo Extrapolation and Allometric Scaling. *Pharmaceutics* **2019**, *11*, 168.
https://doi.org/10.3390/pharmaceutics11040168

**AMA Style**

Choi G-W, Lee Y-B, Cho H-Y.
Interpretation of Non-Clinical Data for Prediction of Human Pharmacokinetic Parameters: In Vitro-In Vivo Extrapolation and Allometric Scaling. *Pharmaceutics*. 2019; 11(4):168.
https://doi.org/10.3390/pharmaceutics11040168

**Chicago/Turabian Style**

Choi, Go-Wun, Yong-Bok Lee, and Hea-Young Cho.
2019. "Interpretation of Non-Clinical Data for Prediction of Human Pharmacokinetic Parameters: In Vitro-In Vivo Extrapolation and Allometric Scaling" *Pharmaceutics* 11, no. 4: 168.
https://doi.org/10.3390/pharmaceutics11040168