Explor Drug Sci EDS Exploration of Drug Science 2836-7677 Open Exploration Publishing 10.37349/eds.2025.1008115 1008115 Original Article A simple quantitative model for the prediction of exposure of renally excreted drugs in pregnant women: a comparison with whole body PBPK model Mahmood Iftekhar Conceptualization Investigation Writing—review & editing * Albericio Fernando Academic Editor University of KwaZulu-Natal, South Africa, Universidad de Barcelona, Spain Mahmood Clinical Pharmacology Consultancy, LLC, Rockville, MD 20850, USA *Correspondence: Iftekhar Mahmood, Mahmood Clinical Pharmacology Consultancy, LLC, Rockville, MD 20850, USA. Iftekharmahmood@aol.com 2025 01 07 2025 3 1008115 16 03 2025 12 05 2025 © The Author(s) 2025. This is an Open Access article licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Aim:

The objective of this study was to develop a simple quantitative model (SQM) to predict maximum plasma concentration (Cmax) and the area under the curve (AUC) of renally excreted drugs (n = 16) in pregnant women from non-pregnant women.

 Methods:

The SQM was developed using 6 physiological parameters and the fraction unbound protein in plasma (fup) as the product characteristic. The six physiological parameters used in this study were total body water, blood volume, cardiac output, glomerular filtration rate (GFR), volume of the fetoplacental unit and blood flow of the fetoplacental unit. A factor was derived based on the average values of the physiological parameters and fup for different gestational ages to predict Cmax and AUC values in pregnant women from non-pregnant women. The predicted values from SQM were then compared with the dedicated clinical studies as well as predicted values by a physiologically-based pharmacokinetic (PBPK) model.

 Results:

Out of 17 Cmax data points, 15 (88.2%), 15 (88.2%), and 12 (70.6%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30-fold prediction error, respectively, by SQM, whereas, 17 (100%), 15 (88.2%), and 13 (76.5%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30 fold prediction error, respectively, by PBPK. Out of 36 AUC data points, 36 (100%), 34 (94.4%), and 30 (83.3%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30-fold prediction error, respectively, by SQM, whereas, 35 (97.2%), 33 (91.7%), and 27 (75%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30-fold prediction error, respectively, by PBPK. The results of the study indicated that the predictive power of both models was very good.

 Conclusions:

The results of the study indicate that the SQM in its predictive performance is as robust and accurate as whole body PBPK.

 Pregnancy simple quantitative model whole body PBPK Cmax and AUC renally excreted drugs Introduction

Several factors can alter the pharmacokinetics (PK) of a drug needing dose adjustment in a given patient population. These factors are generally known as ‘intrinsic’ and ‘extrinsic’ [1]. The examples of intrinsic factors are age, gender, genetics, pregnancy, and disease states such as hepatic and renal impairment [1]. The examples of extrinsic factors are concomitant medicine, smoking, food or beverages (alcohol), malnutrition, water deprivation, and environment [1]. In order to design a safe and effective dose of a medicine in a patient or in a patient population, it is important that both intrinsic and extrinsic factors be taken into account.

Pregnancy leads to substantial anatomical and physiological changes. These changes are important so that the developing fetus can be nurtured for its survival [2]. From the very beginning of conception, these changes begin and affect almost every organ of the body [1, 2].

Significant changes in bodyweight, total body water, blood volume, cardiovascular, glomerular filtration rate (GFR), renal blood flow, and metabolism of a drug can be affected by pregnancy [1, 2]. Total blood volume increases proportionally with cardiac output. The circulating blood volume in pregnancy increases by an average of 45% [3]. An increase in blood volume may lead to decreased concentrations, which may produce the sub-therapeutic effect [4]. Cardiovascular changes start occurring from the early stages of pregnancy. Cardiac output increases by 40% during pregnancy [2, 4]. Pregnancy leads to increased kidney size and weight due to the increased blood volume and vasculature [5, 6]. There is an increase in GFR associated with an increase in creatinine clearance by 30–50% [6]. In short, there are substantial physiological and anatomical changes in pregnancy and these changes may have an impact on the PK characteristics of a drug when administered to pregnant women.

In modern-day drug development, modeling can be helpful in predicting PK parameters and finding suitable dose(s) for ultimate clinical trials in a patient population. Whole body physiologically based-PK (PBPK) models have been suggested [7–9] for the prediction of PK parameters in pregnant women. However, there are examples in the literature that suggest that the whole body PBPK model can be simplified [10–15] to predict PK parameters and dose. Xia et al. [16] suggested a reduced PBPK model to predict AUC of renally excreted drugs in pregnant women (third trimester). Besides using several physicochemical properties and disposition parameters in their model, the authors also used 7 pregnancy-related physiological parameters, and these parameters were body weight, blood volume, cardiac output, volume and blood flow of the fetoplacental unit, volume of total body fat, and GFR.

The objective of this study was to propose a simple quantitative model (SQM) to predict maximum plasma concentration (Cmax) and area under the curve (AUC) in pregnant women from non-pregnant women for renally excreted drugs using 6 physiological parameters and unbound protein concentration in plasma as a product characteristic (Table 1). The predicted Cmax or AUC values by SQM were compared with the observed Cmax or AUC (obtained from dedicated clinical trials) and also with the predicted Cmax or AUC values from the PBPK model to compare the predictive performance of these two models.

Fold change in physiological parameters in pregnant women (compared with non-pregnant women) as a function of gestational age

Parameters (fold change) GA 12 GA 24 GA 30 GA 36
V fetoplacental unit* 5.60 25.67 43.57 63.43
BF fetoplacental unit* 8.02 20.10 25.21 28.17
Ratio (V/BF) 0.70 1.28 2.19 2.25
Blood volume* 1.08 1.29 1.38 1.43
GFR** 1.22 1.41 1.51 1.60
Total body water** 1.12 1.26 1.32 1.39
Cardiac output** 1.17 1.33 1.40 1.48
Sum 5.29 6.57 7.8 8.15
Average 1.06 1.31 1.56 1.63

* Parameter data from [16]. V fetoplacental unit: volume of fetoplacental unit. BF fetoplacental unit: blood flow of fetoplacental unit. Ratio: volume of fetoplacental unit/blood flow of fetoplacental unit. ** Parameter data from [7]. Average consists of Ratio (V/BF), total body water, blood volume, cardiac output, and GFR. The final average for the prediction of Cmax and AUC for a gestational age (GA) was with the fraction unbound protein.

The following linear equations were developed to predict the following physiological parameters as a function of gestational age [7]. This was done because the reported physiological parameters [7] did not match with the gestational age used in this study (GA 12, 24, 30, and 36 weeks).

T o t a l   b o d y   w a t e r = 0.35 × G A + 31.4   ( r 2 = 0.992 )

C a r d i a c   o u t p u t = 3.8 × G A + 308   ( r 2 = 0.982 )

G F R = 1.8 × G A + 118   ( r 2 = 0.901 )

Example

An example of calculation of AUC in pregnant women for digoxin is presented. In order to predict Cmax or AUC for a drug, the fraction unbound protein in plasma will be used as a product characteristic. The fraction unbound protein for digoxin is 0.75. The average for digoxin at GA at week 36 will be 1.48 (average of five ratios in Table 1 plus 0.75 = 1.48). The AUC of digoxin in non-pregnant women was 9.7 ng·hr/mL and in pregnant women in the third trimester or GA 36 weeks, the predicted AUC of digoxin was 9.3/1.48 = 6.3 ng·hr/mL. The observed AUC in pregnant women was 7.3 ng·hr/mL

 Materials and methods

In this study, the SQM was developed using 6 physiological parameters and unbound protein concentration in plasma as the product characteristic (Table 1). The six physiological parameters used in this study were total body water, blood volume, cardiac output, GFR, volume of the fetoplacental unit and blood flow of the fetoplacental unit. These 6 physiological parameters were chosen due to the substantial impact of pregnancy on them. The gestational age was set up as 12, 24, 30, and 36 weeks [16]. The physiological parameter values in Table 1 are presented as fold change in physiological parameters in pregnant women as compared with non-pregnant women and as a function of gestational age [16]. A factor was developed by taking average of the physiological parameter values (fold change from non-pregnant women to pregnant women) along with the fraction unbound protein in plasma for four gestational ages. This factor for the given gestational weeks was then used to predict Cmax and AUC as shown in Equation 1. An example for the calculation of AUC of a drug in pregnant women is shown in the footnote of Table 1.

P r e d i c t e d   C m a x   o r   A U C   i n   p r e g n a n t   w o m e n = O b s e r v e d   C m a x   o r   A U C   i n   n o n - p r e g n a n t   w o m e n   o r   h e a l t h y   v o l u n t e e r s F a c t o r

The predicted Cmax or AUC values by SQM were compared with the observed Cmax or AUC (obtained from dedicated clinical trials) and also with the predicted Cmax or AUC values from the PBPK model to compare the predictive performance of these two models.

Sixteen renally excreted drugs were used in this study to predict Cmax and AUC in pregnant women from Equation 1 in order to validate the predictive performance of the proposed model. The data for these 16 drugs were obtained from the literature [16–23] which had 17 Cmax and 36 AUC values from dedicated clinical trials. In this study, the whole body PBPK models were not developed; rather Cmax and AUC values were taken directly from the published PBPK studies [16–23] for comparison purposes with the SQM. The names of drugs (n = 16) used in this study are described below.

Metformin, digoxin, and emtricitabine [16]; ceftazidime, cefuroxime, ceftriaxone, aztreonam, imipenem, and fluconazole [17]; acyclovir, emtricitabine, lamivudine, and metformin [18]; cefazolin, cefuroxime, and cefradine [19]; oseltamivir [20, 21]; amoxicillin [20]; tenofovir [22, 23].

For drugs used in this study, a comparison was also made by taking the ratios of the observed Cmax and AUC in pregnant women to the observed Cmax and AUC in non-pregnant women. This comparison provided the magnitude of the difference in the exposure parameters between the non-pregnant and pregnant women.

Statistical analysis

Prediction fold-errors of 2 (0.5–2), 0.5–1.5 (a 50% prediction error on either side of 1) and a more stringent criteria in terms of 0.7–1.3 (a 30% prediction error on either side of 1) were used for the assessment of the predictive performance of the proposed SQM. Considering a very high variability in the PK parameters in pregnant women, a 30–50% prediction error may be considered accurate and acceptable from a clinical perspective [24, 25]. The prediction fold error was calculated as follows:

P r e d i c t i o n   f o l d   e r r o r = P r e d i c t e d   P K   p a r a m e t e r O b s e r v e d   P K   p a r a m e t e r

Results

In this study, there were 16 drugs with 53 data points (36 for AUC and 17 for Cmax). The results of this study are summarized below and in Table 2. In Table 3, the Cmax and AUC values in non-pregnant women/healthy volunteers along with dose, and fraction unbound protein, are provided. In Table 4, the observed (from dedicated clinical trials) and predicted Cmax and AUC values by SQM and by whole body PBPK (obtained from the literature) are shown. In Tables 5 and 6, the Cmax and AUC ratios of the studied drugs between pregnant and non-pregnant women are shown. Figures 1 and 2 show a comparison (number of data points versus fold-error) between SQM and PBPK.

A Summary of the number of observations falling within different prediction fold error

Parameters, n Range of prediction fold error Model
SQM PBPK SQM, % PBPK, %
Cmax, n = 17 0.5–2.0 15 17 88.2 100.0
0.5–1.5 15 15 88.2 88.2
0.7–1.3 12 13 70.6 76.5
> 2 2 0 11.8 0.0
AUC, n = 35 0.5–2.0 36 35 100.0 97.1
0.5–1.5 34 33 94.3 91.4
0.7–1.3 30 27 82.9 74.3
> 2 0 1 0.0 2.9

SQM: simple quantitative model

Cmax and AUC values used from non-pregnant women/healthy volunteers to predict Cmax and AUC values in pregnant women

Drugs Dose (mg), non-pregnant Unbound protein Non-pregnant Ref.
AUC, mg·hr/L Cmax, mg/L
Metformin 500 mg oral 0.99 9,804** 1,611* [16, 26]
Digoxin 0.25 mg oral 0.75 9.3** 1.1* [16, 26]
Emtricitabine 200 mg oral 0.96 9.7** 1.4* [16, 26]
Ceftazidime 1,000 mg IV 0.85 150 NA [17]
Ceftazidime 1,000 mg IV 0.85 150 NA [17]
Cefuroxime 750 mg IV 0.67 82 NA [17]
Aztreonam 1,000 mg IV 0.44 166 NA [17]
Ceftriaxone 2,000 mg IV 0.075 1,565 NA [17]
Imipenem 500 mg IV 0.80 33 NA [17]
Imipenem 500 mg IV 0.80 33 NA [17]
Fluconazole 200 mg oral 0.89 175 NA [17]
Acyclovir 400 mg oral QD 0.79**** 3.9 0.80 [18, 26]
Emtricitabine 200 mg QDss oral 0.96 9.8 NA From Vilade et al. in [18] and [26]
Emtricitabine 200 mg QDss oral 0.96 9.8 NA From Vilade et al. in [18] and [26]
Emtricitabine 200 mg QDss oral 0.96 9.8 NA From Vilade et al. in [18] and [25]
Emtricitabine 200 mg QDss oral 0.96 13 2 [18, 23, 26]
Emtricitabine 200 mg QDss oral 0.96 9.7 1.4 From Stek et al. in [18] and [26]
Lamivudine 300 mg QDss oral 0.65 12.7 NA From Benaboud et al. in [18] and [26]
Metformin 500 mg BID 0.99 9.8 1.6 From Eyal et al. in [18] and [26]
Metformin 500 mg BID 0.99 9.8 1.6 From Eyal et al. in [18] and [26]
Metformin 500 mg BID 0.99 9.8 1.6 From Eyal et al. in [18] and [26]
Metformin 500 mg BID 0.99 9.8 NA From Liao et al. in [18] and [26]
Metformin 1,000 mg BID 0.99 9.9 NA From Liao et al. in [18] and [26]
Cefazolin 500 mg IV 0.11 110 NA [19]
Cefuroxime 750 mg IV 0.67 68 NA [19]
Cefuroxime 750 mg IV 0.67 68 NA [19]
Cefradine 500 mg IV 0.80 38.9 NA [19]
Cefradine 500 mg oral 0.80 31.9 11.8 [19]
OC 75 mg oral 0.97 3,507** 397* [20, 21]
OC 75 mg oral 0.97 3,507** 397* [20, 21]
OC 75 mg oral 0.97 3,507** 397* [20, 21]
Amoxicillin 500 mg oral 0.80 20.4*** NA [20]
Amoxicillin 500 mg oral 0.80 20.4*** NA [20]
Tenofovir 300 mg oral 0.93 3.2 0.33 [22, 23, 26]

* Cmax: ng/mL. ** AUC: ng·hr/mL. *** AUC: μg·hr/mL. **** A middle value between 0.09–0.33. BID: twice daily; fup: fraction unbound protein in plasma; OC: oseltamivir carboxylate; QD: once daily; ss: steady state

Predicted and observed Cmax and AUC by SQM and whole body PBPK

Parameters Observed Predicted Ratios
Pregnancy SQM PBPK SQM PBPK
Metformin (3rd trimester) [16]
Cmax (ng/mL) 1,135 1,060 1,068 0.93 0.94
AUC (ng·hr/mL) 6,937 6,450 6,563 0.93 0.95
Digoxin (3rd trimester) [16]
Cmax (ng/mL) 0.8 0.7 0.84 0.88 1.05
AUC (ng·hr/mL) 7.3 6.3 8.0 0.86 1.10
Emtricitabine (3rd trimester) [16]
Cmax (ng/mL) 1.4 0.9 0.94 0.66 0.67
AUC (ng·hr/mL) 8.0 6.4 8.0 0.80 1.0
Ceftazidime; 26.3–33.6 and 37–42 weeks for Caucasian and Japanese, respectively (only AUC values in mg·hr/L [17])
Caucasian 110 143 95 0.86 1.30
Japanese 120 143 104 0.87 1.19
Cefuroxime; 29 weeks (only AUC values in mg·hr/L [17])
Caucasian 42 58 40 1.38 0.95
Aztreonam; 25–30 weeks, from Chinese healthy (only AUC values in mg·hr/L [17])
Japanese 97 121 128 1.25 1.32
Japanese 118 121 142 1.03 1.20
Ceftriaxone; 29 weeks (only AUC values in mg·hr/L [17])
Caucasian 1,588 1,195 1,868 0.75 1.18
Imipenem; 30-32 weeks, from Chinese healthy (only AUC values in mg·hr/L [17])
Japanese 27 22 32 0.82 1.19
Japanese 13 22 32 1.70 2.46
Fluconazole; 7.5 weeks (5–10), Chinese healthy (only AUC values in mg·hr/L [17])
Chinese 121 170 130 1.40 1.07
Acyclovir Cmax (mg/L); 36 weeks for the first dose (1st) and 38 weeks for the rest [18]
400 mg PO, first dose 0.70 0.56 0.62 0.80 0.89
400 mg PO TIDss 0.90 0.56 0.72 0.62 0.80
400 mg PO TIDss 0.74 0.56 0.70 0.76 0.95
200 mg PO TIDss 0.43 0.37 0.34 0.86 0.79
Acyclovir, AUC (mg·hr/L) [18]
400 mg PO, first dose 2.6 2.9 3.7 1.13 1.42
400 mg PO TIDss 3.7 2.9 3.7 0.79 1.00
Emtricitabine [18]
Valade et al.; AUC (mg·hr/L), dose = 200 mg QD
15–28 weeks 8.4 7.8 7.5 0.93 0.89
28–40 weeks 8.2 6.7 7.4 0.82 0.90
39 weeks 8.3 6.7 7.7 0.81 0.93
Colbers et al.; dose = 200 mg QD, 28–38 weeks
Cmax (mg/L) 1.8 1.4 1.5 0.76 0.83
AUC (mg·hr/L) 9.6 8.9 7.6 0.93 0.79
Stek et al.; 31–38 weeks
Cmax (mg/L) 1.4 1.0 1.5 0.78 1.07
AUC (mg·hr/L) 8.0 6.6 7.5 0.85 0.94
Lamivudine; dose = 300 mg PO steady state, 36–40 weeks
AUC (mg·hr/L) 12.5 9.1 10.5 0.73 0.84
Metformin [18]
Eyal et al.; dose = 500 mg PO BID, Cmax (mg/L)
10–14 weeks 1.22 1.45 1.27 1.19 1.04
22–26 weeks 1.06 1.28 1.20 1.21 1.13
34–38 weeks 1.14 1.10 1.23 0.96 1.08
Eyal et al.; dose = 500 mg PO BID, AUC (mg·hr/L)
10–14 weeks 6.5 9.3 8.2 1.37 1.26
22–26 weeks 6.1 7.8 7.7 1.29 1.26
34–38 weeks 6.9 6.7 8.1 0.97 1.17
Liao et al.; dose = 500 mg PO BID; 26–38 weeks
AUC (mg·hr/L) 7.7 6.7 7.9 0.88 1.03
Liao et al.; dose = 1,000 mg PO BID; 26–38 weeks
AUC (mg·hr/L) 11.9 6.7 16.5 0.57 1.39
Cefazolin; 500 mg IV, 19–33 weeks [19]
AUC (mg·hr/mL) 76 83 67 1.10 0.89
Cefuroxime; 750 mg IV, AUC (mg·hr/mL) [19]
13 weeks (11–35 week) 42 48 43 1.15 1.02
42 weeks 47 46 46 0.99 0.99
Cefradine; 500 mg IV, AUC (mg·hr/mL) [19]
15 weeks (10–29) 24 27 26 1.12 1.05
Cefradine; 500 mg oral, 20 weeks (13–33) [19]
Cmax (mg/L) 6.1 7.9 6.2 1.30 1.02
AUC (mg·hr/mL) 25.3 21.4 15.7 0.85 0.62
Oseltamivir Carboxylate, Cmax (ng/mL) [20, 21]
First trimester 150 378 297 2.52 1.98
Second trimester 153 318 270 2.08 1.76
Third trimester 198 272 283 1.37 1.43
Oseltamivir Carboxylate, AUC (ng·hr/mL) [20, 21]
First trimester 1,828 3,340 2,469 1.83 1.35
Second trimester 2,325 2,806 2,226 1.21 0.96
Third trimester 2,367 2,402 2,381 1.01 1.01
Amoxicillin, AUC (μg·hr/mL)
Second trimester 15.2 16.6 24.4 1.07 1.61
Third trimester 14.9 14.0 24.0 0.94 1.61
Tenofovir, third trimester [22]
Cmax (mg/L) 0.28 0.23 0.27 0.81 0.96
AUC (mg·hr/L) 2.5 2.3 1.7 0.91 0.68

SQM: simple quantitative model; ss: steady state; TID: three times daily

AUC values and ratio between non-pregnant/healthy volunteers and pregnant women [16–23, 26]

Drugs Pregnancy Non-pregnant, mg·hr/L Pregnant, mg·hr/L Ratio, preg/non-preg
Metformin 3rd trimester 9,804* 6,937 0.71
Metformin 10–14 weeks 9.8 6.5 0.66
Metformin 22–26 weeks 9.8 6.1 0.62
Metformin 34–38 weeks 9.8 6.9 0.70
Metformin 26–38 weeks 9.8 7.7 0.79
Metformin 26–38 weeks 9.9 11.9 1.20
Digoxin 3rd trimester 9.3* 7.3* 0.78
Emtricitabine 3rd trimester 9.7** 8.0** 0.82
Emtricitabine 15–28 weeks 9.8 8.4 0.86
Emtricitabine 28–40 weeks 9.8 8.2 0.84
Emtricitabine 39 weeks 9.8 8.3 0.85
Emtricitabine 28–38 weeks 13.0 9.6 0.74
Emtricitabine 31–38 weeks 9.7 8.0 0.82
Lamivudine 36–40 weeks 12.7 12.5 0.98
Ceftazidime 29 weeks 150 110 0.73
Ceftazidime 39 weeks 150 120 0.80
Cefuroxime 30–37 weeks 82 42 0.51
Aztreonam 25–30 weeks 166 97 0.58
Aztreonam 25–30 weeks 166 118 0.71
Ceftriaxone 29 weeks 1,565 1,588 1.01
Imipenem 40 weeks 33 27 0.82
Imipenem 40 weeks 33 13 0.39
Fluconazole 30–37 weeks 175 121 0.69
Cefazolin 19–33 weeks 110 76 0.69
Cefuroxime 11–35 weeks 68 42 0.62
Cefuroxime 42 weeks 68 47 0.69
Cefradine (IV) 10–29 weeks 39 24 0.62
Cefradine (oral) 13–33 weeks 32 25 0.78
Oseltamivir First trimester 3,507* 1,828* 0.52
Oseltamivir Second trimester 3,507* 2,325* 0.66
Oseltamivir Third trimester 3,507* 2,367* 0.67
Amoxicillin Second trimester 20** 15.2** 0.76
Amoxicillin Third trimester 20** 14.9** 0.75
Tenofovir Third trimester 3.2 2.5 0.78

* ng·hr/mL. ** µg·hr/mL

Cmax values and ratio between non-pregnant/healthy volunteers and pregnant women [16–23, 26]

Drugs Pregnancy Non-pregnant, mg/L Pregnant, mg/L Ratio, preg/non-pregnant
Metformin 3rd trimester 1.6 1.14 0.71
Metformin 10–14 weeks 1.6 1.22 0.76
Metformin 22–26 weeks 1.6 1.06 0.66
Metformin 34–38 weeks 1.6 1.14 0.71
Digoxin 3rd trimester 1.1* 0.8* 0.73
Emtricitabine 3rd trimester 1.4** 1.4** 1.00
Emtricitabine 28–38 weeks 2.0 1.8 0.90
Emtricitabine 31–38 weeks 1.4 1.4 1.0
Cefradine (oral) 13–33 weeks 11.8 6.1 0.52
Oseltamivir carboxylate First trimester 397* 150* 0.39
Oseltamivir carboxylate Second trimester 397* 153* 0.40
Oseltamivir carboxylate Third trimester 397* 198* 0.52
Tenofovir 38 weeks 0.33 0.28 0.85

* Cmax: ng/mL. ** µg/mL

A comparison of Cmax values (number of data points within fold-error) between SQM and PBPK. SQM: simple quantitative model

A comparison of AUC values (number of data points within fold-error) between SQM and PBPK. SQM: simple quantitative model

Out of 17 Cmax data points, there were 2 data points whose predicted values by SQM were > 2-fold prediction error. All data points by PBPK model were within 0.5–2-fold prediction error. There were 15 data points (88.2%) that were within 0.5–1.5-fold prediction error by both models, whereas 13 (76.5%) and 12 (70.6%) data points were within 0.7–1.3-fold prediction error by PBPK and SQM, respectively (Table 2).

Out of 36 AUC data points, 36 (100%) and 34 (94.4%), and 30 (83.3%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30 fold prediction error, respectively, by SQM, whereas, 35 (97.2%), 33 (91.7%), and 27 (75%) data points were within 0.5–2.0-fold, 0.5–1.5-fold and 0.7–1.30 fold prediction error, respectively, by PBPK (Table 2). The results of the study indicated that the SQM in its predictive performance was as robust and accurate as the whole body PBPK model (Table 2). Overall, predicted Cmax and AUC values in pregnant women reconciled very well with the observed values by both models.

The comparison of Cmax and AUC values between pregnant and non-pregnant women indicated that both exposure parameters were lower in pregnant than non-pregnant women. The AUC and Cmax ratios between pregnant and non-pregnant women ranged from 0.39 to 1.20 (Table 5) and 0.39 to 1.0 (Table 6), respectively. The Cmax ratio between pregnant and non-pregnant women was > 0.6 for 69% of women and > 0.7 for 62% of women. The AUC ratio between pregnant and non-pregnant women was > 0.6 in 88% of women and > 0.7 in 62% of women. The ratios indicate that despite substantial changes in many physiological parameters in pregnant women than non-pregnant women, there is not much impact of pregnancy on the Cmax and AUC values for drugs that are renally excreted.

 Discussion

PBPK models are used for potential application in clinical pharmacology studies to determine PK or dose for special populations such as pediatrics, pregnancy, and renal and hepatic impairment. Over the years, comparative studies between whole-body and minimal or reduced PBPK models have shown that reduced PBPK models are as robust and accurate as whole-body PBPK models [10–15]. A reduced PBPK model uses only a few physiological parameters (as few as 4–5) and is much simpler to develop than a whole-body PBPK model. The comparable prediction accuracy of reduced PBPK models with whole-body PBPK models raises scientific and practical questions about whether the extent of physiological parameters used in a whole-body PBPK model is necessary.

In this study, six physiological parameters and only one parameter in terms of drug characteristic, namely fraction unbound protein in plasma, were used. The objectives of the study were to design an SQM to predict Cmax and AUC of renally excreted drugs for pregnant women without the need for specialized software and extensive data analysis. Pregnancy impacts all physiological parameters [5], and logically, one will consider including all the affected physiological parameters in a model. However, the experience with reduced PBPK models indicates that it is not necessary to use all physiological parameters in a PBPK model rather the model can be substantially simplified [13, 16]. Xia et al. [16] used a minimal physiological model to predict the exposure of 3 renally excreted drugs and one hepatically metabolized drug in the third trimester.

The current study, like previous studies [10–15] clearly indicates that one does not need 10–12 physiological parameters as well as several drug related physico-chemical properties to predict drug exposure in pregnant women. These observations also indicate that the accuracy of the models to achieve the intended objective does not improve by adding complexity or unnecessary parameters (i.e., reduced vs whole body PBPK).

A comparison of the Cmax and AUC values in pregnant women with non-pregnant women indicates that in pregnancy, drug exposure for renally excreted drugs may not be reduced substantially. For the drugs used in this study, the Cmax and AUC ratio between pregnant and non-pregnant women ranged from 0.39 to 1.0 and 0.39 to 1.20, respectively. It can be seen from this study that the change in the magnitude of exposure is highly variable. For many drugs, pregnancy has a negligible impact on the exposure of renally excreted drugs.

Lower exposure of a drug in pregnancy will require dose adjustment in pregnant women and can widely vary. One can also observe different exposure values for the same drugs in different studies. For example, two studies on imipenem in Japanese pregnant women provided two different results [17]. One study indicated that the AUC of imipenem in pregnant women was 82% of that in non-pregnant women and the other study indicated that the AUC of imipenem in pregnant women was 39% of that in non-pregnant women (Table 5).

In pregnancy, the dose adjustment will require a correct estimate of the change in the magnitude of exposure of a given drug. A 2-fold prediction error or even a 50% prediction error from a model may not be acceptable for the selection of the ‘right dose’ in pregnant women. Inaccurate dosing will lead to harmful effects to both the mother and the fetus; hence, a dedicated clinical trial is needed.

It is well established that all models (allometry, physiological, or pharmacometrics) have uncertainty and some degree of inaccuracy because a model’s accuracy is based on the assumptions and information provided to the model. The true biological or physiological mechanisms are barely known; therefore, assumptions are made that may or may not be correct and are generally based on convenience for modeling. In a biological world, models only represent a small fraction of the biological or physiological events that are known. Modeling in a biological system is far more complex than in a physical system. Nevertheless, modeling is a reasonable approach in early drug development and can provide important practical guidance in drug development. Considering the nature of the models, dedicated clinical trials will be needed in pregnant women for the selection of the ‘right dose’.

Simple and pragmatic models, due to the ease of implementation with acceptable predictive performance, are highly desirable and are expected to expedite the development of therapeutic products. This study demonstrates that an SQM using only six physiological parameters and one parameter as a product characteristic can be developed with reasonable accuracy for the prediction of drug exposure in pregnant women. This proposed simple model does not require any specialized software and extensive data analysis rather the entire calculation can be done on an Excel worksheet. The proposed model in pregnancy can support in choosing an appropriate dose in clinical trials to select the right dose to provide therapeutic benefit to pregnant women.

 Abbreviations AUC

area under the curve

 Cmax

maximum plasma concentration

 fup

fraction unbound protein in plasma

 GFR

glomerular filtration rate

 PBPK

physiologically based-pharmacokinetics

 PK

pharmacokinetics

 SQM

simple quantitative model

 Declarations Author contributions

IM: Conceptualization, Investigation, Writing—review & editing.

 Conflicts of interest

The author has no conflict of interest.

 Ethical approval

Data were taken from the literature; hence, ethical approval is not required.

 Consent to participate

Not applicable.

 Consent to publication

Not applicable.

 Availability of data and materials

All data supporting the findings of this study are available within the manuscript and its cited references. Further analytical data are available from the corresponding author upon reasonable request.

 Funding

Not applicable.

 Copyright

© The Author(s) 2025.

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Open Exploration maintains a neutral stance on jurisdictional claims in published institutional affiliations and maps. All opinions expressed in this article are the personal views of the author(s) and do not represent the stance of the editorial team or the publisher.

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