The measurement of C0 has emerged as the standard of care in transplant centers globally. However, the correlation between C0 and AUC has shown varying degrees of reliability across different studies [19]. Recent real-world data analysis of patients in their second and third post-transplant years demonstrated that while both C0 and AUC correlated with BPAR incidence, AUC proved superior in identifying patients with exposure irregularities despite apparently adequate C0 levels [20]. The C0/dose ratio has emerged as a valuable predictor of CNI nephrotoxicity, with studies by Thölking et al. [16, 21, 22] and others [23, 24] demonstrating its prognostic value for renal function outcomes. Fast metabolizers, identified by lower C0/dose ratios, showed higher peak concentrations despite similar trough levels, suggesting that C0 monitoring alone might miss important exposure patterns [17, 25].

Numerous factors have been identified that impact tacrolimus pharmacokinetics, contributing to the inter-patient variability [26–28]. Tacrolimus displays variable absorption in the gastrointestinal tract, with factors like gastric pH, motility, and the presence of food impacting its bioavailability. Reduced absorption can be observed in conditions such as delayed gastric emptying or gastrointestinal inflammation, leading to subtherapeutic drug levels. Gastrointestinal motility disorders, particularly diarrhea, can markedly enhance tacrolimus absorption, potentially leading to toxic levels in certain patients [29–33]. Lemahieu et al mentioned a decreased intestinal p-glycoprotein activity as a potential cause for higher absorption of tacrolimus. Moreover, the accelerated movement through the intestinal tract results in increased tacrolimus exposure to both the distal portion of the small intestine and colonic tissue, where absorption can occur [34]. This drug is extensively metabolized in the liver by cytochrome P450 enzymes, primarily CYP3A4 and CYP3A5, with hepatic function variations significantly altering drug clearance.

Pharmacokinetic variability is further complicated by physiological factors like erythrocyte binding, where lower hematocrit levels result in higher free drug concentrations and increased clearance [27]. Alterations in albumin levels and hematocrit enhance tacrolimus elimination and dosing requirements, although these changes do not substantially impact the unbound drug fraction [27, 35–41].

Patient demographics play a crucial role, with pediatric patients requiring higher doses due to enhanced hepatic enzyme activity, while elderly individuals (≥65 years) experience slower metabolism from age-related liver and kidney function decline, potentially leading to up to 50% higher tacrolimus exposure despite lower dose-to-body weight ratios [42–47].

Drug metabolism through oxidative pathways predominantly involves the Cytochrome P450 (CYP) 3A subfamily, which significantly influences tacrolimus concentrations [44, 45]. CYP3A5*1 (*1 allele expressers) (rs776746) demonstrate markedly increased tacrolimus clearance, requiring approximately 50% higher doses to achieve therapeutic levels compared to non-expressors (*3/*3 genotype) [50–54]. This pharmacogenetic effect underscores the importance of CYP3A5 genotyping in optimizing tacrolimus therapy [2, 50–52, 55]. In contrast, the CYP3A4*22 variant also demonstrates clinical relevance. Carriers of the T variant allele exhibit reduced CYP3A4 activity [56], requiring approximately 33% lower tacrolimus doses [57]. The combined influence of CYP3A4/5 SNPs according to metabolizer phenotypes have significant impact on tacrolimus pharmacokinetic. Different studies have demonstrated that integrating both CYP3A5/4 genotypes can explain over 60% of observed variability in tacrolimus concentrations [57, 58]. Current clinical guidelines from CPIC and IATDMCT [15] recommend increasing doses by 1.5–2 times for patients with enhanced metabolism, highlighting the practical application of this genetic information in personalizing tacrolimus therapy.

Tacrolimus transport is primarily mediated by P-glycoprotein (Pgp), an efflux pump encoded by the ABCB1 gene, which facilitates drug movement across multiple physiological barriers including intestinal epithelium, hepatic tissue, blood-brain barrier, renal tubules, pancreatic cells, and lymphocytic membranes [59]. The ABCB1 gene’s widespread distribution is crucial in determining tacrolimus pharmacokinetics, particularly in absorption, distribution, and elimination [49]. Over 50 ABCB1 SNPs have identified with three key variants in clinical research: 3435C>T (rs1045642), 1236C>T (rs1128503), and 2677G>T/A (rs2032582). These SNPs exist in linkage disequilibrium, suggesting potential coordinated effects on Pgp function. However, despite theoretical expectations of decreased Pgp activity associated with these variants, multiple clinical investigations have failed to demonstrate consistent correlations between these polymorphisms and systemic tacrolimus concentrations [60–65].

Drug-drug interactions with tacrolimus, primarily mediated by CYP3A4 and Pgp, are well-documented [66]. Co-administration of drugs that interact with ABCB1 and/or CYP3A can significantly alter the bioavailability and metabolism of tacrolimus [67]. This may result in high levels of immunosuppression, increasing the risk of toxicity, or in levels that are too low, raising the likelihood of organ rejection [68]. Inhibitors like azole antifungals, calcium channel blockers (e.g., verapamil, diltiazem), HIV protease inhibitors (e.g., ritonavir), macrolides (excluding azithromycin), amiodarone, and nefazodone increase tacrolimus exposure. While azole antifungals are strong inhibitors of tacrolimus metabolism, others, such as azithromycin, have minimal clinical effects. In contrast, inducers like rifampicin, anticonvulsants, and corticosteroids significantly decrease tacrolimus levels. Therefore, in addition to making dosage adjustments, therapeutic drug monitoring (TDM) is essential in clinical practice for transplant patients, especially when changes to their treatment regimen are necessary.

The PopPK approach aims to identify the sources of variability in the pharmacokinetic profile of a drug within the target population, but sufficient data are required. This is a necessary step in the successful clinical translation of any drug. The number of subjects included in the study determines the precision and clinical relevance of the effect of a covariate. PopPK models are compartmental models that describe the dose–concentration relationship from all available data by building a model with structural and statistical components that fits the data (Figure 1). PopPK modeling enables us to optimize the dose regimens, based on the predictive factors of PK variability in the target population.

PBPK models represent a significant advancement over traditional PopPK approaches in their ability to predict drug concentrations across multiple organs. These models integrate both physicochemical properties and physiological characteristics, creating a comprehensive framework based on physiologically meaningful compartments interconnected through blood circulation. The mathematical foundation relies on mass-balance differential equations that precisely define drug movement throughout the system [98].

The architecture of PBPK models demonstrates remarkable flexibility in compartment selection, adapting to specific study objectives. In tacrolimus modeling, particular emphasis is placed on pharmacokinetically significant tissues such as red blood cells, fat, liver, and intestinal tissues, while other less relevant tissues may be consolidated into broader compartments.

Three distinct approaches have emerged in PBPK modeling, each offering unique advantages. The bottom-up approach predicts pharmacokinetics by leveraging drug physicochemical characteristics and in vitro ADME data. This strategy proves particularly valuable when clinical data is limited, with flexibility to be adapted to different populations through physiological parameter adjustments. In contrast, the top-down approach relies heavily on clinical data for model optimization, providing high accuracy for studied populations but with limited extrapolation capabilities. The middle-out approach bridges these methodologies, combining mechanistic and clinical data to enable iterative model refinement.

Model evaluation follows rigorous criteria as outlined in regulatory frameworks [98]. These include detailed comparisons of simulations with experimental concentration-time profiles, utilizing both graphical representations and error function analyses. Models must demonstrate consistency across various scenarios, including different doses, species, populations, and similar compounds. Sensitivity analysis plays a crucial role in identifying key parameters and establishing their plausible ranges.

The importance of PBPK modeling in drug development and clinical applications has been recognized by regulatory bodies, with both the EMA and FDA issuing comprehensive guidance documents for model evaluation. These guidelines, while primarily focused on regulatory applications, provide valuable frameworks that inform broader research applications in human drug modeling.

Machine learning (ML) is a branch of artificial intelligence (AI) that allows computers to learn and make predictions from data without being explicitly programmed to perform each task [111]. Instead of following pre-defined instructions, ML systems use algorithms that analyze data and look for patterns to improve their performance on specific tasks autonomously. The modeling steps consist of: i) data collection and clearing of data for inconsistencies, ii) selection of the best algorithm suitable for the specific purpose (supervised learning, unsupervised learning and reinforcement learning algorithms), iii) training of the model with training data to adjust parameters and learn, iv) performance evaluation of the model with unseen test data, v) optimization of parameters and model deployment in a real-world environment where it can adapt and improve with new data.

PBPK modeling approach offers the possibility of minimizing the animal studies and only using drug-related input parameters for PK predictions in humans. The evaluation of the prediction performance of different software packages as a function of data availability and software options, in a bottom-up approach, showed that predictions are not always within the acceptable range. Moreover, model prediction could not be improved with modeling strategies, but with unbiased parameters used to inform the model [111, 112]. ML is already available to generate unbiased and optimized parameters to be used in bottom-up PBPK modeling approach [113]. The top-down and middle-out approaches can also benefit from AI and ML. For example, AI can contribute to identifying all published PK data of the literature for a drug. Also, these approaches can contribute to optimizations of parameters in the middle-out approach such as tissue Kp values, specific enzyme intrinsic clearance values, or unbound fractions among others. Parameter optimization is particularly labour-intensive and typically not automated, relying heavily on the modeler’s expertise to identify the best-fit parameters. AI and ML could help in this process with ML algorithms. These technologies can test numerous combinations at a speed far beyond human capabilities. Therfore, AI could identify the optimal model configuration that best fits all available clinical data.

ML is still evolving, so that its contribution to advances in MIPD is still scarce. Few ML models have been developed for tacrolimus in renal transplantation with good predictions in both cases. Tang et al [114] used ML to predict stable dose in a large Chinese cohort (N = 1,045 recruited patients, 80% used for the derivation cohort and 20% used for the validation cohort). Among all the ML models, regression tree performed best in both derivation and validation cohorts. Covariates statistically significant in the derivation cohort were CYP3A5 genotype, hypertension and use of omeprazole. Sanchez-Herrero et al also applied ML to predict tacrolimus blood concentrations in a paediatric cohort of renal transplant patients (N = 21) [115]. The ExtraTrees Regressor algorithm had superior performance than the other algorithms tested. In both studies the authors reported acceptable values of metrics used to evaluate the accuracy of predictions. Woillard et al investigated whether ML models (Xgboost) accurately estimated tacrolimus AUC in transplant patients using sparse concentration data [116] and also explored the training of Xgboost ML models on simulated tacrolimus concentration-time profiles [117]. Xgboost machine learning models trained on simulated concentration-time profiles from literature PopPK models enable precise tacrolimus AUC estimation based on sparse concentration data. Further studies are still required to advance on the application of ML on MIPD.

Shin et al evaluated the utility of the ChatGPT4.0 and Gemini Ultra 1.0 large language models for NONMEM coding tasks relevant to pharmacometrics and clinical pharmacology [118]. Their conclusions were that these tools could be useful in the earlier steps to obtain early versions of the codes, but that these codes still require careful checking for errors and improvements before implementation.