Introduction

Overweight (body mass index [BMI] ≥ 25 kg/m2) and obesity (BMI > 30 kg/m2) are increasing worldwide. Clearance (CL) is the primary pharmacokinetic (PK) parameter driving exposure and required drug dosing. Literature suggests that the absolute CL of some drugs increases with obesity (1,2,3,4), while for other drugs CL does not change (5,6,7) or even decreases (8, 9), without single drug properties like elimination pathway being predictive for the nature of these changes (10). Besides, studies on drugs such as propofol (11,12,13,14) or ceftaroline (15) show that the conclusions regarding changes in drug CL with obesity may vary depending on the severity of obesity in the studied subjects. This drug- and patient-dependent variability in changes in CL makes it challenging for clinicians to determine the appropriate drug dosages for subjects with obesity. Due to the complex interplay between different variables, the impact of changes in patient-related variables may be different between different drugs, depending on their drug properties. Therefore, it is important to study which drug- and patient-related variables are influential in driving obesity-related changes in CL.

In practice, dosing methods in obese patients rely either on a flat dose strategy (same dose in obese as in normal-weight subjects) or a bodyweight-based scaling such as allometric scaling with an exponent of 0.75 (AS0.75) or with an exponent of 1 (linear scaling) (10, 16). The accuracy of these dosing methods in the obese population has however not been systematically assessed, particularly not taking different drug properties and severity of obesity into consideration.

Physiologically based PK (PBPK) modeling is ideally suitable to investigate the impact of obesity-related physiological changes on PK parameters, including plasma CL (CLp), for drugs with different properties. As such, this approach can also be used to assess the accuracy of scaling methods for drugs with different properties (17,18,19). In the absence of obesity-related clinical PK data, this can provide a yardstick for scaling drug CLp from normal-weight subjects to those with obesity. This in turn can inform required drug dosing adjustments for this population. Calvier et al. (17) developed a PBPK-based workflow written in R to systematically evaluate the accuracy of scaling approaches for pediatric CLp, which can be extended to other special populations. This workflow can define scenarios in which specific dosing methods are or are not accurate and/or the minimal information required to determine the accuracy of weight-based scaling methods.

In this study, we developed a PBPK-based workflow to study obesity-related changes in CLp in subjects with varying severity of obesity for hypothetical drugs with a wide range of properties that undergo hepatic metabolism, as an extension to the pediatric PBPK-based workflow (17). Within this workflow, the systematic accuracy of commonly used dosing methods is investigated to identify variables under which they yield systematically accurate CLp values.

Materials and Methods

A PBPK-based simulation workflow was developed analogous to the pediatric PBPK workflow published by Calvier et al. (17) using R (version 4.0.3) under R studio (version 1.1.43). This workflow consists of four steps as visualized in Fig. 1 and described below:

Step 1: CLp for Normal-Weight and Obese Subjects

Fig. 1
figure 1

Schematic representation of the physiologically-based pharmacokinetic simulation workflow. CLp, hepatic plasma clearance; BW, body weight; PE, prediction error

Full size image

Drug-Specific Parameters

A total of 17,600 hypothetical drugs undergoing hepatic metabolism were generated using all possible combinations of the following drug-specific properties with realistic ranges defined for normal-weight individuals (18, 20,21,22): 1) the unbound drug fraction in plasma (fu), which ranged from 1 to 100%, with eight equidistant intermediate values; 2) the type of drug binding plasma protein, for which the drugs were assumed to exclusively bind to either human serum albumin (HSA) and α1-acid glycoprotein (AAG); 3) blood-to-plasma partition coefficient (Kp), which varied between 0.35 and 40 with 11 different values (i.e. 0.35, 0.8, 1, 2, 3, 4, 5, 10, 20, 30 and 40) (23, 24); and 4) the unbound intrinsic CL value for one microgram of liver microsomes (CLint,mic), which reflects both isoenzyme affinity and abundance and which ranged from 0.56·10−6 to 0.209·10−3 mL·min−1·μg−1 microsomal protein with 100 equidistant intermediate values.

Subject-Specific Parameters

PBPK simulations were performed for a representative normal-weight subject with a BMI of 20 kg/m2, as well as for five representative subjects with varying class of overweight or obesity, with BMIs of 25, 30, 40, 50, and 60 kg/m2. The weight for these subjects was calculated based on their BMI and a typical height of 1.72 m, which is the median height for adults in the National Health and Nutrition Examination Survey (NHANES) database (25). This yields a bodyweight of 59.2 kg for the normal-weight subject and 74.0, 88.8, 118.3, 148.0, and 177.5 kg for the overweight and obese subjects, respectively.

Subject-specific parameters for each representative subject, including hepatic blood flow (Qh), plasma concentrations for HSA and AAG, hematocrit, liver weight, and milligram protein per gram of liver (MPPGL) were calculated based on the equations reported by Berton et al. (26). The demographic characteristics of the typical subjects implemented in the PBPK-based simulation workflow and their corresponding subject-specific parameter values are provided in supplemental Table S1. Obesity-related change in fu, total hepatic intrinsic clearance (CLint), and blood-to-plasma ratio (B:P) were calculated using Eq. 1–3, respectively.

$${fu}_{obese}=\frac{1}{1+\frac{\left(1-f{u}_{normal-weight}\right)\times {PP}_{obese}}{{f{u}_{normal-weight}}_{ \times }{PP}_{normal-weight}}}$$
(1)
$${CL}_{int}={CL}_{int,mic}\times MPPGL\times Liver\; weight \times rEA$$
(2)
$$B:P = 1+(Hematocrit*(fu*{K}_{p}-1))$$
(3)

In these equations, funormal-weight, CLint,mic and Kp were taken from the values for the hypothetical drugs for the normal-weight subject as defined above. PP is the concentration of plasma protein which was assumed to be either HSA or AAG. According to the equations reported by Berton et al. (26), PP and liver weight vary with BMI while hematocrit remains constant (supplemental Table S1). In the absence of information on changes in Kp, this parameter was assumed to remain constant across the BMI range. Consequently, the impact of obesity on B:P is solely attributable to fu. As it is unknown how obesity impacts the CLint,mic of the hepatic enzymes, scenarios with different relative enzyme activity (rEA) in obesity were investigated. For this, rEA values of 40%, 60%, 80%, 100%, 120%, 140%, 160%, and 180% of normal enzyme activity were selected, which is in line with reported changes in the obese on the basis of in vitro data (27). Here, a rEA value of 100% indicates no change in enzyme activity compared to normal-weight subjects.

PBPK Model

The dispersion model (Eq. 4–7) was used to obtain PBPK-based CLp values for all drugs and all subjects defined above. This model was selected as it has been reported to predict hepatic CLp more accurately than the well-stirred model for highly cleared drugs, while both models lead to equivalent clearance predictions for other drugs (28).

$$CLp={Q}_{h}\times ER\times B:P$$
(4)
$$ER=1-\frac{4a}{{(1+a)}^{2}exp\left\{(a-1)/{2D}_{N}\right\} - {(1-a)}^{2}exp\left\{-(a+1)/{2D}_{N}\right\}}$$
(5)
$$a={(1+4{R}_{N}\times {D}_{N})}^{1/2}$$
(6)
$${R}_{N}= (fu/B:P)\times {CL}_{int}/ {Q}_{h}$$
(7)

In these equations, CLp is the total hepatic metabolic plasma clearance, Qh is the hepatic blood flow, ER is the extraction ratio, B:P is the blood-to-plasma ratio, fu is the unbound drug fraction in plasma, CLint is the total hepatic intrinsic clearance, RN is the efficiency number, and DN is the axial dispersion number for which a value of 0.17 was used (29).

After the CLp was generated for the representative subjects, relative CLp in the obese was calculated according to Eq. 8, reflecting obese CLp as a percentage of normal-weight CLp. Correlations between the relative CLp in the obese and drug or subject characteristics were investigated to identify the influential variables for predicting CLp for subjects with obesity.

$$Relative\; obese\; CLp=\frac{{CLp}_{obese}}{{CLp}_{normal-weight}}\times 100\%$$
(8)

Step 2: Calculating the Allometric Scaling Exponents for the Obese

For each drug and each obese subject, the allometric exponent that accurately scales CLp from the normal-weight value, was calculated using Eq. 9 and the bodyweights (BW) of the normal-weight subject and the obese subjects. Correlations between the exponent and drug or subject characteristics were visually inspected.

$$Exponent= \frac{{\text{ln}}({CLp}_{obese}/{CLp}_{normal-weight})}{{\text{ln}}({BW}_{obese}/{BW}_{normal-weight})}$$
(9)

Step 3: Systematic Accuracy of Dosing Methods

Scale obese CLp from Normal-Weight CLp using Different Dosing Methods

For each hypothetical drug, the normal-weight CLp from step 1 was used to scale CL to obese subjects, using three commonly used bodyweight-based dosing methods (i.e., AS0.75, linear scaling and flat dosing). All three methods can be described using Eq. 10:

$${Scaled \;CLp}_{obese }={CLp}_{normal-weight}\times {\left(\frac{{BW}_{obese}}{{BW}_{normal-weight}}\right)}^{exponent}$$
(10)

In Eq. 10, the following three values were used for the exponent:

  1. 1)

    0.75, this is also known as fixed allometric scaling and will be referred to as AS0.75,

  2. 2)

    1, this is known as linear scaling, or

  3. 3)

    0, this is known as flat dosing, which yields a constant CLp value that does not change with bodyweight.

Assess Scaling Accuracy

For each drug and each obese subject (defined by a unique combination of BMI and rEA), the accuracy of the three dosing methods was assessed. This was performed using the prediction error (PE) according to Eq. 11, with scaled CLpobese corresponding to the CLp scaled from normal weight to obese using one of the three scaling methods, and CLpobese corresponding to the PBPK-based CLp in obese subjects. Patterns in PE were assessed visually. Systematic scaling accuracy was defined as PE values of all hypothetical drugs being within ± 30%.

$$PE\left(\%\right)=\frac{{Scaled \;CLp}_{obese}-{CLp}_{obese}}{{CLp}_{obese}}\times 100\%$$
(11)

Results

Variables Correlating With Changes in CLp in Obese Subjects

The relative CLp of all hypothetical drugs for the obese subjects with various BMI and rEA are shown in supplemental Table S2. Its correlations with subject characteristics and drug properties are illustrated in Figs. 2 and 3. These results demonstrate how subject characteristics and drug properties are correlated with obesity-related changes in CLp.

Fig. 2
figure 2

Correlation between the relative plasma clearance (CLp) of subjects with body mass index (BMI) of 25, 40 and 60 kg/m2 and (a1-a2) intrinsic clearance, (b1-b2) unbound drug fraction in plasma (fu), and (c1-c2) hepatic blood flow for drugs bound to human serum albumin (HSA, left panel) and a1-acid glycoprotein (AAG, right panel). Colors represent different extraction ratios. Note that the values of fu and extraction ratio represent the values defined for the normal-weight subject. Some colors are overlapping

Full size image
Fig. 3
figure 3

Correlation between the relative plasma clearance (CLp) of subjects with body mass index (BMI) of 25, 40 and 60 kg/m2 and representative relative enzyme activity for all hypothetical drugs with (a) low extraction ratio (ER), (b) intermediate ER, and (c) high ER. Blue and pink areas represent drugs that bind to human serum albumin (HSA) or a1-acid glycoprotein (AAG), respectively. The purple area represents drugs not binding to plasma proteins. The grey area represents all hypothetical drugs, allowing comparisons between the three plots of the same BMI. The red dotted line represents the scenario of no change in enzyme activity. Note that the values of the ER represent the values defined for the normal-weight subject

Full size image

Regarding subject characteristics, BMI is found to be strongly correlated with CLp changes in obese subjects. Table S2 indicates a significant increase in relative CLp with increasing BMI values. For the situation where there is no change in enzyme activity (i.e., rEA is 100%), the relative CLp in the obese varies from a value as low as 106% in overweight subjects with a BMI of 25 kg/m2 to a maximum of 244% in morbidly obese subjects with a BMI of 60 kg/m2. However, it is noteworthy that for overweight subjects with a BMI of 25 kg/m2, the change in CLp for all drugs was not more than 17%, suggesting a limited change in CLp compared to the normal-weight subjects.

The correlations between relative CLp in the obese and BMI are illustrated in Figs. 2 and 3. Figure 2 shows that as BMI increases, CLint and hepatic blood flow all increase, albeit with varying magnitude, and that their correlations with obese relative CLp become more pronounced. The rEA is an obesity-related physiological variable that is considerably correlated to changes in CLp in obese subjects, as can be seen in Table S2 and Fig. 3. When rEA varies from 40 to 180%, the relative CLp in the obese increases approximately 4-, 2.5-, and 1.5-fold for drugs with low, intermediate, and high ER, respectively. It should be noted that relative CLp decreases only when enzyme activity decreases.

In terms of drug properties, Fig. 2 provides insights into the correlation between relative CLp in the obese with fu, in the absence of changes in enzyme activity. As fu and ER of drugs may change with obesity, in the description of drug properties these parameter values will refer to the values defined for each drug in the normal-weight subject. The patterns of the correlation between relative CLp in the obese and fu differ between HSA- and AAG-bound drugs. For HSA, with fu of a drug increasing in normal-weight subjects, the relative CLp in the obese is decreasing, especially when BMI is higher than 40 kg/m2. For AAG this is the other way around. In addition to that, the differences between HSA- and AAG-bound drugs become more pronounced as BMI increases. Besides, the relative CLp in the obese in HSA-bound drugs is generally higher than that of AAG-bound drugs. Moreover, as depicted in Fig. 2, when CLint increases, the relative CLp in the obese only slightly changes for AAG-bound drugs. In contrast, an evident decline is observed in HSA-bound drugs, particularly among morbidly obese subjects.

The degree of hepatic ER of a drug in normal-weight subjects also shows a strong correlation with CLp changes in obese subjects. As shown in Table S2, a narrower range in relative CLp in the obese is found for drugs with high ER compared to drugs with low ER (range of 62.6 – 215 versus 42.5 – 458), indicating that when ER is high, the relative CLp is less variable and less dependent on obesity. Moreover, as shown in Figs. 2 and 3, the correlation between ER and relative CLp is found to be more pronounced in subjects with higher BMI, especially in drugs with low to intermediate ER. Finally, these figures indicate that the correlation between ER and CLp is highly dependent on the type of drug binding plasma protein. For HSA-bound drugs, relative CLp in the obese is generally lower for drugs with high ER than for drugs with low ER, but this is not evident in AAG-bound drugs.

Scaling Exponents for the Obese

The allometric exponents for all hypothetical drugs are presented in supplemental Table S3 and are illustrated in Fig. 4, categorized by BMI, rEA and drug properties. The correlations between the exponent and various drug properties or subject characteristics align with the correlations observed with the relative CLp in the obese.

Fig. 4
figure 4

Correlation between the exponent in the allometric equation (see Eq. 9) yielding perfect plasma clearance (CLp) scaling and representative relative enzyme activity for subjects with body mass index (BMI) of 25, 40 and 60 kg/m2 for all hypothetical drugs with (a) low extraction ratio (ER), (b) intermediate ER and (c) high ER. Blue and pink areas represent drugs that are bound to human serum albumin (HSA) or a1-acid glycoprotein (AAG), respectively. The purple area represents drugs not binding to plasma proteins. The grey area represents all hypothetical drugs, allowing comparisons between the three plots of the same BMI. The red dotted line represents no change in enzyme activity. Black dotted lines represent 0 and 1, the extreme values of the tested exponent values. Note that the values of the ER represent the values defined for the normal-weight subject

Full size image

According to Table S3, the exponent that yields perfect scaling of obese CLp values, ranges from -3.84 to 3.34 and is impacted strongly by rEA. In the absence of changes in rEA, the exponent ranges from 0.244 to 0.851 and decreases when the enzyme activity of a drug decreases in normal-weight subjects. Furthermore, as shown in Fig. 4, drugs binding to AAG generally have a lower exponent compared to drugs binding to HSA, and drugs with higher ER generally have a smaller exponent compared to those with a lower ER.

Systematic Accuracy of Dosing Methods

The accuracy of the predicted CLp values in the obese obtained using the three different dosing methods (i.e., AS0.75, linear scaling, and flat dosing) was assessed using PE values and is provided in Table S4. Figure S1-3 shows the accuracy of the three dosing methods, respectively AS0.75, linear scaling and flat dosing, and illustrate that none of the three methods can be universally applied.

Of the three investigated dosing methods, all of them are generally systematically accurate for subjects with overweight or obesity with a BMI below 30 kg/m2, with unchanged or up to 50% increased enzyme activity (Figure S1-3). In any of the other cases, information on the drug binding plasma protein, ER, fu, and relative change of enzyme activity is required to select an appropriate dosing method for the obese. Specifically, as shown in Figure S3, if the drugs bound to AAG have high ER, flat dosing performs generally accurately, regardless of the class of obesity. For drugs with low to intermediate ER, AS0.75 or linear scaling are more accurate, especially when there is a large (i.e., more than 60%) increase in enzyme activity for drugs binding to HSA (Figure S1-2). When enzyme activity is reduced, flat dosing tends to be more accurate, especially for drugs binding to AAG.

Discussion

This study utilizes a PBPK-based framework that was written in R and uses the most recent literature on physiological changes related to obesity to predict drug CLp in subjects with different class of overweight and obesity, considering a diverse set of hypothetical drugs that undergo hepatic metabolism. This approach yields quantitative insights into the correlation between drug properties and subject characteristics on changes in CLp in obesity. Furthermore, this study evaluates the systematic accuracy of commonly used weight-based dosing methods and identifies scenarios where these methods may or may not yield systematically accurate predictions.

This study investigates the physiological mechanisms driving pharmacological changes in CLp in obese subjects, offering a basis for the interpretation of reported literature findings. For instance, El-Baraky et al. found unaltered CLp of propofol in the obese (11) while others reported increased CLp (12,13,14). These seemingly contradictory findings can be explained by our results shown in Fig. 2c1, indicating that changes in CLp for propofol, an HSA-bound drug with high ER, are significant only in morbidly obese subjects with a BMI higher than 40 kg/m2, a population that was not included in the study of El-Baraky et al. The result can be explained by the fact that for drugs with a high ER, CLp is less sensitive to alterations in enzyme activity and is more limited by hepatic blood flow (10). Hepatic blood flow changes as a function of the severity of obesity, as quantified by BMI. Significant alterations in hepatic blood flow become evident only when there are substantial changes in BMI, resulting in notable differences in CLp.

Besides, increased CLp of paracetamol has been reported in obese subjects (4). This can be attributed to changes in CYP2E1, the major enzyme involved in paracetamol metabolism, which is reported to be increased in obese individuals, resulting in increased CLp. Conversely, literature reported a decrease in CLp in obese subjects for clozapine (8, 9), likely due to the reduced activity of CYP3A4, the principal enzyme responsible for clozapine metabolism, leading to a decrease in CLp. It should be noted, however, that the existing literature contains limited information on quantitative change of enzyme activity in the obese population. Therefore, we defined relative changes in obesity-induced enzyme activity compared to normal enzyme activity. The range of these relative changes was selected so that it can encompass potential scenarios of decreased enzyme activity (e.g. CYP3A4) as well as increased enzyme activity (e.g. CYP2E1) in overweight and (morbidly) obese subjects (27). The generic nature of the applied functions for the relative change in enzyme activity can also be used to assess the impact of changes in enzyme activity driven by other factors, like for instance polymorphisms or drug-drug interactions. When quantitative data regarding obesity-induced alterations in specific enzyme activities become available, our results can be used to predict corresponding changes in CLp for drugs with different properties and in subjects with different severity of obesity.

Drug properties, such as fu, drug-binding protein, and ER, also correlate with obese CLp. For fu, we found that with fu of the normal weight subject increasing, the change in CLp decreases for HSA-bound drugs, but increases for AAG-bound drugs. This may seem counterintuitive, since with decreased HSA concentration and increased AAG concentration in the chronic inflammatory state caused by obesity (20, 22, 26), the fu increases for HSA-bound drugs and decreases for AAG-bound drugs in obese subjects compared to normal-weight subjects. However, supplemental Figure S4 shows that as fu in normal-weight subjects increases, the relative change in fu between obese and normal-weight subjects for AAG-bound drugs increases, while it decreases for HSA-bound drugs. Consequently, this leads to less CLp change for HSA-bound drugs and a more pronounced CLp change for AAG-bound drugs. Regarding ER, it is known that CLp in drugs with low ER is dependent on multiple variables, such as fu and CLint. The narrower range of CLp changes with increasing ER may result from intricate interplay of multiple variables in drugs with a low ER causing more substantial variability in CLp change compared to drugs with a high ER, which are influenced mainly by hepatic blood flow. Intriguingly, the correlation between hepatic ER and CLp is notably seen in HSA-bound drugs, with the relative CLp in the obese lower for drugs with high ER compared to low ER. This is likely due to increased fu in obese subjects as HSA concentration decreases, causing alterations in ER for HSA-bound drugs. Specifically, a low ER in normal-weight subjects increases to an intermediate (or high) ER in the obese, while a high ER in normal-weight subject remains high in the obese, resulting in limited changes in CLp for drugs with a high ER. Conversely, for AAG-bound drugs, the decrease in fu with obesity partially counteracts the effects of other variables that contribute to the increase in CLp, resulting in a reduced CLp change between drugs with high and low ER.

BMI and rEA contributes to considerable variability in the changes of CLp in the obese population. This variability leads to a wide range of exponent values yielding perfect scaling. However, in most scenarios, the exponent that yields perfect scaling remains within the range of zero to one. Of three investigated dosing methods, all of them are generally systematically accurate for subjects with overweight or obesity with a BMI below 30 kg/m2, with unchanged or up to 50% increased enzyme activity. In any of the other cases, information on the drug binding plasma protein, ER, fu, and relative change of enzyme activity is required to select an appropriate dosing method for the obese, as no single scaling method is universally accurate when dealing with the complex interplay of different drug properties and obesity severity. The figures provided in this paper can guide more detailed assessments of the accuracy of scaling methods in specific scenarios.

Through this PBPK approach, we identify the theoretical boundaries of allometric exponents when scaling CLp to the obese and the PE for commonly used scaling methods. The following assumptions are important for the interpretation of our findings and could be further expanded on in future research. Firstly, the assumption made in this work is that hepatic metabolism is the sole elimination pathway of the hypothetical drugs. In this work, this does allow for a ‘clean’ assessment of the impact of changes in parameters relevant to this clearance route. However, in real life, CLp may be impacted by multiple clearance routes, including renal or biliary excretion, which have not been included in the framework. Moreover, as the impact of obesity on the expression and activity of transporters involved in hepatic CLp remains unavailable, we assumed no transporter involvement in the hepatic clearance. The current framework could be extended to include this information once this information becomes available. Information on potential obesity-related changes in MPPGL is also not yet available, we therefore assumed this to remain unchanged (26). According to Eq. 2, a specific percentage of changes in MPPGL would impact the CLp in the same way as the same percentage of changes in rEA. The presented work can therefore still be used to assess the potential impact of obesity-related changes in MPPGL. Besides, it has been suggested that dynamic free fraction leads to a greater free fraction for drugs and allows for better predictions of CLint in human compared to in vitro CLint,mic (30). Once the data becomes available for obese subjects, utilizing dynamic free fraction would likely yield superior results. Moreover, this study generated a total of 17,600 hypothetical drugs to capture all possible combinations of the drug properties with realistic ranges. This enables us to explore a wide combination of drug properties, offering systematic insights into the relevance and optimal ranges of these properties. It is important to note, however, that Kp values are typically lower than one. Finally, the height of all representative subjects was assumed to be 1.72 m when deriving their bodyweight from BMI. This value was selected as it is the average height from the NHANE database (25). We also tested a height of 1.85 m and presented these results in the Supplemental Figure S5-6. These results indicate that the assumption made on subject height barely impacts our conclusion.

Conclusion

In subjects with obesity, the exponent of an allometric covariate function for CLp, has a wide range of values depending on BMI, enzyme activity, and drug properties (i.e., fu, drug binding plasma protein, and ER). AS0.75, linear scaling and flat dosing methods are generally systematically accurate for subjects with overweight or obesity with a BMI below 30 kg/m2, with unchanged or up to 50% increased enzyme activity. In any of the other cases, information on the different drug properties and the severity of obesity is required to select an appropriate dosing method for the obese.