1. Introduction

Saudi obesity estimates differ by measurement and standardisation. A 2020 telephone survey estimated weighted obesity prevalence at about one quarter [1], while subsequent surveillance described self-reported trends [2]. The NCD-RisC analysis published in 2024 estimated age-standardised 2022 obesity at 38.1% for men and 48.3% for women in Saudi Arabia [3]. Age-standardised estimates must not be interpreted as crude national prevalence. We use them solely to define a reproducible historical simulation scenario.

Obesity changes body composition, blood flows and drug disposition, and the effect is drug-specific [4, 5]. A single weight descriptor cannot therefore be assumed to perform well for all drugs. Simulation can explore consequences of explicit physiological assumptions, provided that extrapolation and uncertainty are distinguished from clinical validation.

Theophylline is a useful test case for this problem. It is a methylxanthine bronchodilator with a narrow therapeutic window, conventionally 10–20 mg/L, and adverse effects that become more frequent as plasma concentrations rise [6]. Its role has narrowed as inhaled therapies have improved, but it remains a low-cost option for airway disease [6]. Saudi asthma management guidance is updated regularly [7], and theophylline continues to be evaluated as an add-on therapy in chronic obstructive pulmonary disease [8]. Theophylline also has unusually rich obesity pharmacokinetic data. In the late 1970s and 1980s, several groups reported its distribution volume and clearance in obese and non-obese adults [9, 10, 11, 12, 13, 14]. These studies did not agree on the best weight descriptor. Some favoured TBW for loading doses [9], others IBW [11, 13], and one fitted an empirical power function of TBW [12]. They supply independent clinical observations that a mechanistic model can be tested against, but they do not show how dosing rules would perform across the BMI distribution of the present Saudi population.

PBPK models separate drug properties from organ volumes, flows and tissue composition [15]. Obesity applications include oncology and paediatric examples published by 2025 [16, 17]. Regulatory guidance recommends explicit reporting of context, inputs, estimation and predictive performance [18]. Here, the model is evaluated against observed data before exploratory application; unsuccessful clearance qualification is retained as a substantive limitation.

We aimed to evaluate a theophylline PBPK model against open individual data and independent obesity summaries, then compare weight scalars in a 2022 age-standardised Saudi BMI scenario. This is a simulation-based comparison of model behaviour, not development of a clinical dosing recommendation.

2. Methods

2.1 Design, context of use and reporting

The study has model estimation, external evaluation and exploratory application stages. Reporting follows FDA recommendations for PBPK analyses [18]. The replacement of population inputs by the archived 2024 release was an editorial correction made after the original analysis, not a prespecified change. No new human participants were enrolled.

2.2 Data sources

The drug, physiology and individual concentration inputs were retrieved on 6 November 2026. During editorial correction, the 2026-updated WHO BMI files were removed and replaced by Saudi rows from the archived NCD-RisC 2024 dataset. The replacement files and extracted rows were preserved with checksums. Retrieval in 2026 is distinguished from the evidence publication date.

(i) Compound and system parameters came from the open-source R package httk, version 2.7.4 [19]. It provided the theophylline record (molecular weight, octanol:water partition coefficient, acid dissociation constant, fraction unbound in plasma, blood:plasma ratio, in vitro hepatocyte intrinsic clearance and fraction absorbed), human tissue composition data from Schmitt [20], tissue volumes, tissue blood flows [21] and the calibration regression of Pearce and colleagues [22].

(ii) Individual concentration–time data came from R datasets::Theoph. This is an open dataset of 12 adults who received a single oral theophylline dose of 3.1–5.86 mg/kg and had 11 serum samples each over about 25 h (132 samples in total). Body weights ranged from 54.6 to 86.4 kg.

(iii) External qualification targets were group means transcribed from four independent published studies of theophylline in obese and non-obese adults: Gal and colleagues (14 obese and 57 normal-weight adults) [9], Blouin and colleagues (12 markedly obese patients) [10], Rohrbaugh and colleagues (8 lean and 8 obese subjects) [11], and Rizzo and colleagues (40 asthmatic patients weighing 45–176 kg) [12]. None of these data were used to estimate model parameters.

(iv) The revised population inputs are sex-specific 2022 age-standardised prevalences of BMI <18.5, 25 to <30 and ≥30 kg/m² from the NCD-RisC Lancet 2024 archived country dataset [3]. These are standardised to a reference age distribution and are not crude resident-population prevalences. Published NCD-RisC height means of 167.7 cm for men and 155.9 cm for women were retained [23].

2.3 Model structure

The model comprised 14 flow-limited compartments: venous and arterial blood, lung, adipose tissue, bone, brain, gut, heart, kidney, liver, muscle, skin, spleen and a remainder compartment. A gut lumen depot was added for oral dosing. Gut and spleen drain into the liver through the portal vein. The reference total hepatic blood flow was 87.0 L/h, and the hepatic arterial flow was obtained by subtracting gut and spleen flows. The reference cardiac output was 336.0 L/h. The concentration in blood leaving each tissue was the tissue concentration multiplied by the blood:plasma ratio and divided by the tissue:plasma partition coefficient (Kp). Elimination was hepatic and described by the well-stirred liver model. The unbound intrinsic clearance was scaled from the in vitro hepatocyte value using 110 × 106 hepatocytes per gram of liver and the predicted liver mass, after correction for binding in the incubation (fraction unbound in the incubation 0.955) [24]. Renal excretion of unchanged theophylline is minor and was absorbed into total clearance. Because every process was first order, the system was linear and was solved exactly with matrix exponentials rather than numerical integration.

2.4 Drug-specific inputs and partition coefficients

Table 1 lists the drug-specific inputs and their sources [24, 25, 26, 27, 28, 29]. Tissue Kp values were first predicted mechanistically with the Schmitt method [20], using membrane affinity estimated from lipophilicity [25]. They were then adjusted with the Pearce calibration regression, which is the default in httk and was developed to correct systematic bias of the uncalibrated Schmitt method [22]. Uncalibrated Kp values were retained as a sensitivity analysis.

Table 1. Drug-specific and system parameters of the theophylline physiologically based pharmacokinetic model.

Values in parentheses are 95% bootstrap confidence intervals (500 resamples of subjects). log P, logarithm of the octanol:water partition coefficient; pKa, negative logarithm of the acid dissociation constant; SD, standard deviation; SF, empirical multiplier applied to the in vitro–in vivo extrapolated intrinsic clearance. The reference individual is a man weighing 70 kg with a height of 1.76 m.

2.5 Body composition and scaling to obesity

For each individual, LBW was calculated with the Janmahasatian equations [30], IBW with the Devine equations [31], and AdjBW as IBW plus 0.4 times the excess of TBW over IBW. Fat mass was TBW minus LBW. The volumes of all lean organs, plasma volume and the remainder compartment were scaled in proportion to LBW relative to the reference LBW of 56.1 kg. Adipose volume was calculated from fat mass and adipose density. Lean-tissue blood flows were scaled with the 0.75 power of the LBW ratio. Adipose blood flow was assumed proportional to adipose volume, and cardiac output was the sum of tissue flows. Hepatic intrinsic clearance therefore rose with liver mass and, through it, with LBW. This scaling assumption was tested in external qualification rather than fitted.

2.6 Middle-out parameter estimation and internal evaluation

A purely bottom-up model was first simulated with no empirical adjustment. Three parameters were then estimated for each Theoph subject by minimising squared log-residuals: the absorption rate constant, the clearance scaling factor and a single global scalar applied to all Kp values. The partition-coefficient scalar was not prespecified. It was added post hoc, after the bottom-up model was seen to overpredict distribution volume in these data, and it scales all tissues equally; obese-population data were never used to choose or estimate it. The pre-dose sample of each subject was excluded, leaving 120 post-dose observations. Each subject's own body weight was used; height was not recorded and was set to 1.76 m. Population values were geometric means across subjects, and between-subject variability of clearance was the standard deviation of the log scaling factor. Predictive performance was assessed by leave-one-subject-out cross-validation. Each subject's profile was predicted from population values estimated on the remaining 11 subjects, and we summarised the average fold error, the absolute average fold error, the proportion of concentrations within two-fold and 1.25-fold, and predicted-to-observed ratios of area under the curve and peak concentration [32]. Parameter uncertainty was quantified by bootstrapping subjects (500 resamples).

2.7 External qualification in obesity

The qualified model was used, without further adjustment, to simulate typical men (1.76 m) and women (1.63 m) matching the body-size characteristics reported in each external study, and sex-averaged predictions were compared with the published group means. For the study by Gal and colleagues, the mean ratio of TBW to IBW in the obese group (2.02) was derived from the reported volume per kg of TBW and per kg of IBW. For the study by Blouin and colleagues, the corresponding ratio (1.86) was derived from the reported clearance values. For the study by Rohrbaugh and colleagues, mean body weights (57.0 kg lean and 88.8 kg obese) were derived from the reported volumes in litres and per kg. The apparent distribution volume during the terminal phase was compared with the published apparent volumes. We also compared predicted distribution volume for typical men (1.72 m) and women (1.60 m) across TBW from 45 to 176 kg with the empirical power function reported by Rizzo and colleagues (volume = 1.29 × TBW^0.74). The prespecified criterion for adequate prediction of a group mean was a predicted-to-observed ratio between 0.8 and 1.25; ratios within two-fold were also reported.

2.8 Virtual Saudi adult population

For each sex, a log-normal BMI distribution was fitted to the three archived 2022 age-standardised category probabilities. Height was drawn around the published sex-specific mean with assumed SD 6.5 cm and truncation 140–200 cm; BMI was truncated to 16–70 kg/m². We generated 1,500 virtual men and 1,500 virtual women. The resulting 50:50 mixture is an assumed comparison scenario, not a demographic representation of Saudi Arabia. The three category inputs do not fully determine the tails of the true BMI distribution; the log-normal assumption is additional.

2.9 Dosing scenarios, outcomes and uncertainty

Each virtual adult received an intravenous loading dose of 5 mg/kg over 0.5 h followed by a continuous infusion of 0.4 mg/kg/h. In turn, the weight in mg/kg was TBW, AdjBW, IBW or LBW. The primary outcomes were the proportions of adults with plasma concentrations of 10–20 mg/L at the end of the loading infusion and after 72 h of maintenance. Secondary outcomes were the proportions above 20 mg/L and below 10 mg/L, analysed overall and by BMI class (below 25, 25–29.9, 30–34.9, 35–39.9 and 40 kg/m² or more). A narrower range of 5–15 mg/L was used as a sensitivity analysis. Parameter uncertainty was propagated by re-simulating 200 bootstrap replicates of the population clearance scaling factor, its variability and the partition-coefficient scalar on random subsamples of 600 virtual adults. The 2.5th and 97.5th percentiles across replicates were reported as 95% uncertainty intervals. Local sensitivity analyses in a reference woman with a BMI of 40 kg/m² (97.3 kg, 1.56 m) varied the fraction unbound in plasma (±20%), the blood:plasma ratio (1.0 versus 1.33), log P (±1 unit), the acid dissociation constant (7.82 versus 8.8) and the clearance scaling factor (95% confidence limits).

2.10 Software

All analyses were performed in Python 3.13 with NumPy 2.5.3, SciPy 1.18.1 (matrix exponentials, least-squares and Nelder–Mead optimisation), pandas 2.3.3 and Matplotlib 3.11.2. R data objects were read with the rdata package. A single script reads only the frozen inputs and regenerates every number, table and figure.

3. Results

3.1 Bottom-up prediction and partition coefficients

Without empirical adjustment, the model predicted a plasma clearance of 5.62 L/h and a steady-state volume of 0.672 L/kg for the 70-kg reference man. In leave-out comparison with the Theoph data, bottom-up predictions showed an average fold error of 0.559 and an absolute average fold error of 1.898, with only 61.7% of concentrations within two-fold. The uncalibrated Schmitt method predicted an adipose Kp of 0.955. The Pearce calibration lowered this to 0.46 but raised the liver and kidney values above 2 (Table 2).

Table 2. Predicted tissue:plasma partition coefficients of theophylline.

Kp, tissue:plasma partition coefficient. The final model multiplies the calibrated values by the global partition-coefficient scalar of 0.571 estimated from the Theoph data. The calibration regression is not applied to the remainder compartment.

3.2 Middle-out estimation and internal evaluation

The estimated population clearance scaling factor was 0.471 (95% confidence interval 0.398–0.533). Between-subject variability in clearance corresponded to a coefficient of variation of 27.1%. The global partition-coefficient scalar was 0.571 (0.517–0.625), and individual estimates ranged from 0.422 to 0.803. The population absorption rate constant was 1.08 h^-1. Individual clearances ranged from 19.2 to 54.6 mL/h/kg (median 41.8 mL/h/kg), and the median individual steady-state volume was 0.432 L/kg. For the reference man, the qualified model predicted a clearance of 2.72 L/h, a steady-state volume of 0.428 L/kg and a terminal half-life of 7.7 h. The bottom-up clearance was therefore 2.07-fold higher than the clearance supported by the observed data.

In leave-one-subject-out prediction, the average fold error was 1.041 and the absolute average fold error was 1.304. Of the held-out concentrations, 93.3% fell within two-fold and 55.0% within 1.25-fold (Figure 1). The geometric mean predicted-to-observed ratio of the area under the curve was 1.014 (range 0.61–1.39); all 12 subjects were within two-fold and 9 within 1.25-fold. For peak concentration, the geometric mean ratio was 0.947, with 9 subjects within 1.25-fold.

Figure 1. Internal qualification of the theophylline model against the open Theoph dataset. (A) Observed serum concentrations after a single oral dose (points; 12 adults) with the median and 90% interval of 200 simulated adults of similar body weight receiving 4.5 mg/kg. (B) Leave-one-subject-out predicted versus observed concentrations on logarithmic axes; the solid line is identity and the dashed lines mark two-fold limits.

3.3 External qualification in obesity

Only 8 of 14 external metrics met the prespecified 0.8–1.25 prediction criterion. All seven volume metrics met that criterion; clearance was systematically underpredicted, with ratios about 0.56–0.79. All metrics happened to lie within the secondary two-fold range, but that broader result does not override failed prespecified clearance qualification. The model is therefore partially evaluated for distribution and insufficiently qualified for absolute maintenance exposure. The volume comparison with the Rizzo function and the partition-coefficient sensitivity remain descriptive (Table 3 and Figure 2).

Table 3. External qualification of the theophylline model against independent published obese and non-obese adult studies.

Ratio, predicted divided by observed group mean. CL, total plasma clearance; IBW, ideal body weight; t1/2, terminal elimination half-life; TBW, total body weight; Vd, apparent volume of distribution (model value: terminal-phase volume). Observed values are group means from the cited abstracts [9, 10, 11]; none were used for parameter estimation.

Figure 2. External qualification of predicted theophylline disposition across body size. (A) Predicted terminal-phase volume of distribution for typical men (1.72 m) and women (1.60 m) across total body weight (TBW), compared with the published power function of Rizzo and colleagues and with simple proportional scaling at 0.482 L/kg. (B) Predicted-to-observed ratios for 14 published group means; the shaded band marks 0.8–1.25. CL, clearance; HF, heart failure; IBW, ideal body weight; t1/2, half-life; Vd, volume of distribution.

3.4 Virtual Saudi population

The revised log-normal scenarios fitted prevalences of BMI ≥25 and ≥30 kg/m² of 72.2% and 38.4% in men, versus archived inputs 72.7% and 38.1%, and 75.2% and 48.6% in women, versus 75.8% and 48.3%. Median fitted BMI was 28.2 and 29.7 kg/m². The fitted ≥40 kg/m² tails were 4.5% and 12.2%; these are model-derived tails, not observed national prevalence. The 3,000 virtual adults had 42.7% obesity, 8.5% BMI ≥40 and median weight 75.5 kg (5th–95th percentile 49.9–113.7).

Revised disposition summaries are shown in Table 4. Across the lowest to highest BMI class, median Vss/TBW decreased from 0.422 to 0.372 L/kg, CL/TBW from 35.700 to 24.387 mL/h/kg, while CL/IBW increased from 36.401 to 53.827 mL/h/kg. Median terminal half-life increased from 8.153 to 10.642 h. These are model predictions under specified physiology and variability assumptions.

Table 4. Predicted theophylline disposition in the virtual Saudi adult population by body-mass-index class.

Values are medians. BMI, body mass index; CL, total plasma clearance; IBW, ideal body weight; LBW, lean body weight; n, number of virtual adults; t1/2, terminal half-life; TBW, total body weight; Vss, volume of distribution at steady state.

Figure 3. Revised 2022 age-standardised Saudi BMI simulation scenario. Left: simulated BMI in 1,500 virtual men and 1,500 virtual women; right: weight-normalised disposition summaries by BMI class. The mixture and distribution shapes are assumptions, not a sample of Saudi patients. Vss/TBW is multiplied by 100 for display, as labelled; clearance units are mL/h/kg.

3.5 Target attainment of dosing scalars

TBW- and AdjBW-based loading put 100% of the 3,000 simulated adults within 10–20 mg/L under the model assumptions. In the highest BMI class, median end-loading concentrations were 17.0 and 11.5 mg/L respectively; IBW gave 7.9 mg/L and no simulated individual in range. No claim of 100% clinical success follows: loading concentrations depend strongly on the represented distribution volumes, and interindividual partition-coefficient variability was not fully modelled.

At 72 h, TBW gave 71.7% in range overall, with 7.4% above 20 mg/L. At BMI ≥40, TBW gave 74.4% in range (95% parameter uncertainty interval 49.0–98.0) and 22.8% above 20 mg/L. AdjBW gave 60.1% in range overall; at BMI ≥40 it gave 61.8% in range (43.9–81.4), 0.4% above and 37.8% below 10 mg/L. IBW gave 13.4% in range in that class. These intervals propagate estimated parameter uncertainty and Monte Carlo subsampling, not all physiological or structural uncertainty.

Against the alternative 5–15 mg/L target, maintenance attainment at BMI ≥40 was TBW 40.5%, AdjBW 87.4%, IBW 93.7%, LBW 95.7%. The scalar ranking depends on the chosen target and unresolved clearance bias.

Table 5. Proportion of virtual Saudi adults within 10–20 mg/L by dosing scalar, overall and in the highest body-mass-index class.

Regimen: intravenous loading dose of 5 mg/kg over 0.5 h followed by 0.4 mg/kg/h, with mg/kg referring to the stated scalar. AdjBW, adjusted body weight (IBW + 0.4 × [TBW − IBW]); BMI, body mass index (kg/m2); IBW, ideal body weight; LBW, lean body weight; TBW, total body weight; UI, uncertainty interval across 200 bootstrap replicates of population parameters. Results for all BMI classes are given in the supplementary table.

Figure 4. Revised target attainment by BMI class using archived pre-2026 evidence. Bars show proportions within 10–20 mg/L at end-loading and 72 h; vertical lines show 95% parameter-bootstrap intervals from 200 replicates. The results are conditional simulations rather than clinical dose recommendations.

3.6 Sensitivity analyses

In the reference woman with a BMI of 40 kg/m² (97.3 kg) receiving IBW-based dosing, the predicted steady-state volume was 36.5 L and clearance 2.36 L/h. Across the local sensitivity analyses, the 72-h concentration ranged from 6.9 to 10.2 mg/L, compared with a base value of 8.3 mg/L. The fraction unbound in plasma and the clearance scaling factor had the largest influence (72-h concentration 9.7 and 7.3 mg/L at the lower and upper scaling-factor limits). Varying log P by one unit changed the steady-state volume from 29.189 to 59.773 L but changed the 72-h concentration little. The blood:plasma ratio had a negligible effect (steady-state volume 34.9 versus 36.5 L).

4. Discussion

4.1 Principal findings

The revised application replaces post-2025 population evidence with the archived 2024 release describing a 2022 age-standardised Saudi BMI scenario. The full model calculation and 200-replicate uncertainty analysis were rerun. Dosing scalars produced different exposures, but external evaluation supports distribution volumes more strongly than clearance. The failure of the prespecified clearance criterion limits maintenance interpretation; the simulation cannot establish which scalar is clinically optimal.

4.2 Comparison with previous studies

The results agree with the most consistent message of the clinical theophylline literature. Gal and colleagues found that distribution volume per kg of TBW was similar in obese and normal subjects and recommended TBW for loading [9]. The model reproduced their obese-group volume almost exactly and showed why: theophylline distributes mainly into body water, and adipose partitioning is low, but not negligible, relative to lean tissue. The empirical exponent of 0.74 reported by Rizzo and colleagues [12] lies between proportional scaling and no scaling, and the model's exponent of 0.87 kept predicted volumes within about 11% of their function over the full weight range. In contrast, the uncalibrated Schmitt partition coefficients implied more than proportional scaling of volume with TBW. With them, the model would have overpredicted volume by up to 68% at the highest weights. This finding is consistent with the known bias of the uncalibrated method for hydrophilic compounds and with the purpose of the Pearce calibration [22]. The conclusion of Rohrbaugh and colleagues [11] that IBW should be used for loading was based on a smaller obese group with a lower volume per kg of TBW; the model predicted that group's volume 25% higher. Zahorska-Markiewicz and colleagues likewise favoured IBW [13]. Some of the disagreement among the historical studies may therefore reflect small samples and differences in body composition, which a mechanistic model can address directly.

Historical studies differ in smoking, disease and body size, which can affect theophylline clearance [10, 14, 34, 35]. The model underestimated clearance and did not resolve these covariates. Demographic scaling of liver mass cannot be assumed to capture obesity-related enzyme activity [15]. These differences remain unresolved rather than being corrected by labelling all predictions within two-fold.

The bottom-up clearance discrepancy illustrates the limitations of in vitro–in vivo extrapolation [27]. Empirical adjustment was reported transparently and obesity summaries were not used to fit parameters. That separation prevents direct reuse of the external targets for estimation, but does not make a model qualified when the prespecified criterion fails. The post hoc partition-coefficient scalar and the publication-cutoff correction are explicitly identified.

4.3 Implications for Saudi practice

The age-standardised scenario is relevant to methodological questions in Saudi settings but does not estimate the distribution or dosing needs of current patients. Loading comparisons depend on the assumed distribution model; maintenance comparisons are additionally biased by underpredicted clearance. Neither the simulated target proportions nor the apparent ranking should be used for patient-specific dose selection. Local observed concentrations, comorbidities, smoking and therapeutic drug monitoring are needed before a clinical application.

4.4 Strengths and limitations

Strengths include open inputs, separation of estimation from external evaluation, a reproducible archived pre-2026 population source, explicit reporting of failed qualification and rerunning the revised population scenario with parameter uncertainty.

Limitations include abstract-level historical external targets, absent height/sex/smoking covariates in Theoph, a post hoc global partition scalar, incomplete clearance qualification and unrepresented variability in organ partitioning. The BMI source is age-standardised, the 50:50 sex mixture and log-normal tails are assumed, height variability is assumed, and no age-specific prevalence weights are modelled. Bootstrap intervals omit important structural and physiological uncertainty. No Saudi patient concentration data were used to validate the model. The results describe conditional pharmacokinetic simulations, not efficacy or toxicity in patients.

4.5 Future research

Future work should use Saudi therapeutic drug monitoring data with measured height, weight, age, smoking, comorbidity and interacting medications. The clearance model should be evaluated and improved against independent observations before maintenance predictions are used clinically. An age-specific resident-population model could replace the present standardised comparison scenario.

5. Conclusions

A theophylline PBPK model reproduced published distribution volumes more closely than clearance. Reanalysis using the archived NCD-RisC 2024 evidence produced a 2022 age-standardised Saudi BMI comparison scenario. Weight scalars changed predicted exposure, but incomplete clearance qualification, assumed population structure and incomplete variability preclude clinical dosing recommendations.

Declarations

Funding: NA

Conflicts of Interest: NA

Institutional Review Board Statement: This study used only publicly available, de-identified data and published summary statistics; no human participants were recruited and no ethics approval was sought or claimed.

Informed Consent Statement: Not applicable (public de-identified data).

Data availability: Theoph individual concentration data, httk-derived physiology and compound inputs, published height estimates and archived NCD-RisC Lancet 2024 BMI country estimates were used. The archived population source is https://ncdrisc.org/archives.html, with Saudi 2022 rows from NCD_RisC_Lancet_2024_BMI_age_standardised_country.csv. Publication year is 2024; retrieval and revised calculation occurred in 2026. The former WHO 2026-updated input files are not used in the revised application.

Author Contributions: NA

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