Opportunities for machine learning and artificial intelligence in physiologically-based pharmacokinetic (PBPK) modeling

Abstract

Physiologically-based pharmacokinetic (PBPK) modeling is a powerful tool for quantitating and understanding the fate of drug and drug carriers in complex living systems. It is particularly valuable in situations where data are difficult to obtain due to cost, time, or ethical constraints. Recent advances in PBPK modeling have greatly improved their accuracy in modeling in vivo and clinical data, especially in special populations (e.g., pediatric and geriatric subjects), which consequently enhanced their utility in drug development. Nevertheless, current PBPK models remain limited by our ability to ascertain complex biological mechanisms and/or physiological processes, often resulting in many critical but unknown parameters or parameters with large uncertainty. Machine learning (ML) and applications of broader artificial intelligence (AI) tools that facilitate parameter estimation, model learning, database mining, and uncertainty quantification not only offer the potential to address the shortcomings of PBPK modeling, but also introduce opportunities for enabling earlier use of PBPK modeling in the drug development process. Here, we summarize ML-influenced advances in PBPK modeling and discuss our expectations of the likely avenues for future ML/AI contributions to PBPK modeling.

Introduction

Physiologically-based pharmacokinetic (PBPK) modeling provides a mass-balanced means to track and predict the biodistribution of drugs and drug carrier systems (referred to collectively as “drugs”). By considering each organ or tissue type of interest as a compartment, a multi-compartment model can be constructed to recapitulate the fate of drugs in complex living systems, with the drug dosage form (including route of dosing) and the dose serving as the key inputs, and drug concentration profile over time at each organ/compartment serving as the key outputs^1,2. By accounting for key processes in living systems, drug properties, and drug-environment interactions, PBPK modeling not only helps to ensure direct physiological relevance of its predicted drug concentrations but also yields valuable insights into drug interactions or exposures that cannot be easily established in vitro ^1,3. Finally, with the incorporation of known pharmacological understanding of a drug’s potency, PBPK models can also predict a drug’s pharmacodynamic (PD) profile^4,5.

By separately accounting for the various key underlying biological and physiological processes, different parameters and ordinary differential equations (ODEs) can be easily introduced, enabling PBPK models to more accurately scale and predict across species from small to large animals to eventually humans, as well as between different subpopulations (e.g., infants vs. adults)⁶. Not surprisingly, PBPK models have been used extensively to characterize and quantitatively predict the biodistribution and PK profile of various small molecule drugs^7,8, therapeutic proteins and antibodies^9–11, as well as nanoparticles^12–18 and other drug delivery systems^1,19–21. Each of these systems requires unique considerations accounting for whether the drug’s transport processes are primarily perfusion, diffusion or permeability-limited, as well as how the resulting drug distribution is affected by inherent properties of the drug, including polarity, hydrophobicity/solubility, charge, and chemical/biological stability. In addition to the development of new drugs, PBPK models have also been used to aid in the assessment of potential bioequivalence for generic drugs and biosimilars²². Recently, the utility of PBPK models has been extended to vaccine development, including evaluation of injected adjuvants and oral delivery of both antigen and adjuvant^23–25. Finally, PBPK models are increasingly utilized for evaluating potential toxicity, drug interactions, and how the body may process the drugs in special populations where data are often limited or unavailable (e.g., pediatrics or patients with chronic illness)^26–31.

There is an increasing push to minimize the use of preclinical animal models for assessing the safety and efficacy of drug candidates^32–34. Similarly, in silico drug discovery is also enjoying increasing popularity, with virtual chemical library screening offering the potential of reduced time and costs while improving the accuracy of candidate selection^35,36. By definition, drug molecules must reach and persist in sufficient concentrations at the target disease cells or tissues over time to achieve therapeutic benefit, and they preferably do so at concentrations in target cells/tissues that exceed those in other cells or tissues to minimize systemic side effects. Thus, in addition to a differentiated pharmacological mechanism of action, an accurate accounting of the distribution and fate of drugs is undoubtedly a critical element in advancing computational medicine. We consider PBPK modeling to be the leading computational approach that bridges early-stage drug discovery through preclinical animal models to human studies.

While incorporating greater physiological and biological insights should improve the accuracy of PBPK modeling, doing so with an already large parameter space undoubtedly creates further challenges with parameter uncertainty. Among the strengths of artificial intelligence (AI) and machine learning (ML) techniques are their ability to inform ways to reduce the parameter space, which in turn reduces the complexity and increases the tractability of the problem, as well as their ability to increase our confidence in the estimated values of the most sensitive parameters. Below we discuss in detail the current limitations of the PBPK modeling space, techniques for applying AI/ML to PBPK, successful applications of these techniques, and the future of AI/ML in PBPK models from our perspective.

Challenges and Limitations of PBPK models

Despite the promise and success of PBPK modeling, the PBPK modeling field faces many challenges, which we elaborate below:

Dependence on known processes and quantities

A current limitation of PBPK models is their reliance on known parameters describing various physiological processes, as well as a drug’s physiochemical quantities that in turn influence its absorption, distribution, metabolism, and excretion (ADME). These parameters naturally vary not only for different drugs but also for different drug delivery systems as well as individuals, and thus are often not available a priori. Accurate measurements of many metabolic or transport processes are difficult to obtain, as they must either involve invasive experimentation or be subjected to the risks of poor in vitro to in vivo correlation ³⁷. Often, measurements of metabolic or transport processes do not directly translate across different living species. Indeed, despite the extensive and broadly accepted use of allometry to translate from a mouse or large animal to a human system, and recent work suggesting improvements to allometric models by deviating from the traditional 3/4 power law for metabolic scaling, there remain frequent disparities between predictions derived from preclinical animal models and observed pharmacokinetics (PK) and biodistribution in humans^38–41. Experimentation also takes time and money, and is often ethically restrictive, which greatly reduces the rate new drugs can be advanced into a clinical setting. Recently, QSAR (quantitative structure-activity relationship) models have been used to address the challenge of obtaining clinically relevant parameters as inferred from their physiochemical properties. However, the QSAR process itself is inherently dependent on the availability of, and ability to leverage, large data sets to draw reliable, drug-specific conclusions from the underlying structure-function model. Many of these QSAR approaches are mainly for general exploration purposes^42–45 and thus frequently fail to achieve high accuracy⁴⁶, although recent model iterations are yielding improved applicability⁴⁷. There thus remains substantial room for improving its efficiency.

Rapidly compounding model complexity to capture relevant biological processes

To illustrate one example of the biological complexities faced with developing a PBPK model, we consider a PBPK model for a therapeutic immunoglobulin (IgG) as described by Garg and Balthasar¹¹. Within each tissue compartment, the antibody first leaves the bloodstream (vascular space), then enters the endosomal vesicles in the endothelial cells via endocytosis or pinocytosis. From there, IgG may form high affinity bonds with the neonatal Fc-receptor (FcRn) as a result of the low endosomal pH, which allow FcRn-bound IgG to either be recycled back to the vascular space or transported into the interstitial space. IgG can also be transported directly between the vascular and interstitial space via two-pore paracellular transport^48–50. The IgG can leave the organ through lymphatic flow, leave through vascular flow, or be cleared from the system in a saturable target-specific manner (often referred as target-mediated drug disposition). Within each compartment, such a model requires knowledge of blood flow rate, lymph flow rate, residual blood volume, endosomal fraction of the organ, interstitial fraction of the organ, total tissue volume, dissociation constant for IgG:FcRn binding stoichiometry as a function of pH, expression level of FcRn, endocytosis rate, recycling rate for bound IgG, and transport rate for unbound IgG. Although many of these parameters have either been measured or estimated, the values used across different models can vary by orders of magnitude. For example, the fraction of lymph flow to blood flow has been estimated as both 0.02%⁴⁹ and 2%⁵¹, due in part to varying tissue composition. Other considerations include tracking cell-associated fraction beyond the interstitial space, as proposed by Covell et al.⁵¹, Shah and Betts⁵², and Abuqayyas and Balthasar⁵³, as well as focusing on preferential distribution due to target antigens⁵³, approaches which further add to the number of unknowns per compartment. Extrapolating to a full model comprised of additional selected compartments – including plasma, heart, liver, spleen, kidney, muscle, lung, small intestine, large intestine, pancreas, gallbladder, bone, brain, adipose, thymus, thyroid, skin, and tumor – further increases the complexity of the parameter estimation by over an order of magnitude (Figure 1).

Figure 1.

Schematic of PBPK system for therapeutic antibodies in circulation and within each organ compartment.

Further complexities with modeling different formulations and simultaneous use of multiple medications

To adapt or develop a PBPK model to predict the fate of a nanoparticle-based drug delivery system instead of a therapeutic antibody, we would need to first account for major discrepancies in known processes (e.g. extravasation, endocytosis, etc.). We would also then need to account for entirely new processes, such as (i) uptake by the mononuclear phagocytic system, which is frequently responsible for a high degree of inter-patient variability observed in clinical studies¹², and (ii) specific and non-specific uptake by various cells. Accounting for passive and active transport processes of nanoparticles remains an area for further investigation for PBPK models^12,54–56. If the nanoparticle is a drug carrier, the release and separate tracking of the released small molecule drugs must also be layered on top of the model, further increasing the complexity of the system and number of required parameters.

It is possible to take another step and harness PBPK models to predict potential deleterious drug-drug interactions. Although most physiological parameters are translatable, a full set of drug-specific parameters for a second drug must be determined or estimated. One must also account for effects of either drug on specific biological processes, such as inhibition of metabolizing enzyme cytochrome P450⁵⁷. Given that many patients, particularly the elderly, are chronically taking several medications simultaneously, the complexities of harnessing PBPK models to predict polypharmacy challenges can readily increase exponentially.

Limited data availability

We then consider limitations due to data availability, in the form of local drug concentrations among different cells and tissues. The aforementioned need to account for a large number of physiological processes by definition requires quantitative description of the various parameters that underpin the respective processes. To determine the predictive power of a PBPK model, it is also essential to validate whether the predictions are accurate. This necessitates measuring actual drug concentrations in various organs over time. This is generally accomplished by sacrificing animals and harvesting key organs at select time points, followed by processing of tissues and analyzing the resulting content using high-performance liquid chromatography, ELISA, or mass spectroscopy. Alternatively, to minimize the number of animals that must be sacrificed or to improve the accuracy of longitudinal assessment, relative concentrations at whole organ levels could be determined in large organs in live animals using in vivo detection techniques such as positron emission tomography/computed tomography (PET/CT). Regardless of the approaches, such experimentations range from very expensive to cost-prohibitive, generally yield only small batches of data, and typically do not provide insights at the sub-organ and cellular levels. Given differences in not only the assays but also inter-laboratory variability, it is often difficult to piece together data available from multiple published studies. Data available in the literature is also often scattered across sources, not readily available or accessible for modeling.

Another key challenge faced in PBPK model development is validating model predictions in patients early on, particularly in subpopulations where these models likely have the greatest potential for impact (e.g., pediatrics or rare disease patients). Notably, these subpopulations often lack suitable animal model substitutes, and thus are poorly supported by animal studies. The use of genetically identical animals also makes it difficult to capture the degree of inter-patient variability observed in clinical settings. Additionally, while existing PBPK models hold great value for modeling drugs administered by infusion or injection, there are far fewer models for alternative delivery systems and routes of dosing, such as topical application or inhalation. Understanding these systems and associated routes of delivery is an area with much room for PBPK models to expand in. PBPK modeling’s inherent capacity to incorporate the detailed physiology of the system and information on complex drugs makes them particularly apt for this purpose, whereas the inherent complexity of the system is well suited to harness AI to construct and validate such models.

Limited pre-existing information on processes and parameters in complex systems

Given the aforementioned difficulty of obtaining in vivo PK or ADME data, ascertaining the best model or scaling properties to capture the fate of new drugs in specific target organs must typically be accomplished without complete or accurate knowledge of all parameters. To overcome this uncertainty, one must consider a set of potential candidate models describing the drug distribution behavior, and corresponding parameters in each of the models, many of which include a wide range of potential values. Such a process necessitates a method to systematically and iteratively evaluate candidate models against known biodistribution data and narrow the ranges for each parameter. Over time, this allows us to infer the most important physiological process (i.e., those with greatest impact on PK predictions) or drug-specific parameters based on the learned model structure and parameter values, and simultaneously increases our confidence in the model predictions for drug concentrations over time.

AI/ML techniques applicable to PBPK modeling

While not novel techniques in and of themselves, many AI/ML algorithms have novel applications in PBPK modeling. We summarize them below:

Latin Hypercube Sampling (LHS) and other parameter estimation techniques

LHS is an optimization technique traditionally used in problems across engineering and biological systems ^58–63. LHS works by conducting “layers” of random sampling, i.e., sampling a range and then a point within the range. For example, let’s assume one wants to test combinations of values or “sweep” for one parameter that is expected to range from 0.1–0.5 (dimensionless units) and a second variable between 1.2–1.7. The LHS technique would divide this into partitions of 0.1–0.2, 0.2–0.3, etc. and 1.2–1.3, 1.3–1.4, and so on. One then shuffles the partitions, selects a value within each partition to test in combination, and repeats this process several times until arriving at a combination of parameters that yields predictions with the lowest error compared to experimental data. If potential parameter values span large ranges, one could sweep logarithmically to cover partitions across orders of magnitude. The LHS technique ensures more equitable sampling across the entire parameter search space, and simultaneously minimizes the chance of randomly picking points too close together.

The random sampling approach with LHS lends itself well to the parameterization of PBPK models to ensure a thorough search of parameter space. For example, a PBPK model parameterized with LHS has accurately recapitulated the biodistribution of PEGylated liposomes and proteins in mice and humans^58,64. Strategically integrating a sensitivity analysis, such as Partial Rank Correlation Coefficients (PRCC), extended Fourier amplitude sensitivity test (eFAST), or one-at-a-time (OAT) sensitivity, with a sampling algorithm enables testing which components of the system most critically impact the behavior or property of interest, particularly in large multiscale systems ⁶⁵. Iterating LHS or combining it with another optimization approach, such as Sobol Sequencing, Hammersley Sequence Sampling, or gradient descent, leads to increased confidence that the model converges to a solution with minimal error, particularly when a large number of unknown parameters are involved^66,67. When combined with supervised learning, sampling methods such as LHS (i.e., through conditioned LHS (cLHS) or Progressive LHS (PLHS)) can yield large advantages in computational efficiency without sacrificing accuracy of parameterization⁶⁸.

Monte Carlo (MC) parameter estimation and model learning

In their simplest sense, MC methods refer to random sampling of variables from a defined distribution or set of distributions. Applications include defining a distribution for each parameter in order to represent a range of potential drug properties, representing population variance, establishing a means of uncertainty quantification for risk analysis, and defining in silico experiments that assist in the design of preclinical studies and clinical trials^69–71. Such methods have been employed in population-level PBPK studies measuring exposure and bioaccumulation^72–75. Markov Chain Monte Carlo, or MCMC, is a variant of MC sampling in which the distribution of values sampled is dependent on previous samples⁷⁶. MCMC is used in Bayesian or likelihood inference⁷⁷, and represents a strategic way to iteratively refine estimated parameter values for PBPK modeling and simulation⁷⁴. Notable subclasses of MC include importance sampling and particle filtering. Importance sampling leverages weighting or sampling from transformations of expected parameter distributions to ultimately achieve convergence at a parameter’s estimated value or distribution. Also known as sequential importance sampling, particle filtering is a method of assigning weights based on the inferred likelihood of a parameter value, given the intersection of multiple potential distributions^78,79. While traditionally implemented in risk analysis or statistics, these techniques have been applied for parameter identification at the population level when there is low confidence at the individual level^80,81, and are utilized in parameter calibration algorithms for systems biology⁸².

Sampling techniques, including MC and LHS, become “learning” when parameter values, distributions, or model structures are sampled, evaluated, and modified accordingly. In addition to its applications in parameterization, an MC approach to model learning can fundamentally influence our understanding of a biological system in which we must make assumptions about the most appropriate physiological processes and the corresponding functional form incorporated into PBPK (e.g., the relative importance of an organ subcompartment, or to discern whether convective or diffusive transport is dominant). In such cases, biodistribution data and an initial parameter set based on in vitro studies or a literature search for similar characterized drugs are used to initialize a suite of candidate models. The goal is to search not only for a set of parameters, but to arrive at a model or set of models that, when fitted with optimized parameters or well-characterized parameters, generates predictions most consistent with the data^83,84. Commonly used in applications ranging from information theory to finance, these methods are robust in that they can potentially compensate for sparse data sets^84,85.

In not only learning parameter values but also improving the model structure itself while attempting to minimize errors with model outputs, we can frequently gain insights into the mechanistic underpinnings of how specific drugs are distributed and processed in the body. For example, evaluation of competing PBPK models may emphasize the role of flow limitation within a compartment in providing more accurate predictions than the previously assumed well-mixed system⁸⁶. Such insights inform more targeted experiments for future data collection, for instance, which compartments or organ systems should be prioritized for sampling in future studies. MC models are also valuable for assessing the degree and sources of variability between individuals^71,87. As previously discussed in the context of LHS, implementing a global sensitivity analysis platform is an efficient means of refining the model where little is known about a system and data are difficult to obtain^88,89. Bayesian techniques have been successfully incorporated and combined with MCMC to uncover sources of uncertainty at the population level⁷¹.

Ensemble modeling

Another valuable strategy, when data are especially sparse or mechanistic understanding is lacking for the system of interest, is consensus or ensemble modeling. In ensemble modeling, a large number of different models (generally more phenomenological than mechanistic) are tested and evaluated, with the goal of obtaining a set of candidate models that can produce an accurate readout of biodistribution or other metric of interest. While each top model candidate is individually incorrect, each model does capture some aspect of the system, and the models collectively produce the desired behavior. Since ensemble modeling is based on the assumption that we can leverage a set of models rather than one ground truth to describe the desired phenomena, the goal is typically more outcome-oriented than mechanistic. However, the candidate models could still inform our mechanistic understanding of the system.

The ensemble strategy is implemented when uncertainty regarding the model structure is not resolved, but we can infer a purely data-driven prediction and propose a large number of model candidates. Since we have limited understanding of the system in this scenario, using these models together provides the greatest predictive power. These concepts have previously been applied in fields as diverse as genomics, weather forecasting, predicting traffic flow patterns, and credit scoring^90–94. Expanding into the PBPK space holds valuable implications for accurately predicting drug properties or interactions with high confidence. For example, an ensemble strategy has been demonstrated to successfully predict not only parameter values but also the distribution and dissolution profiles of drugs in humans^95,96. Implementing an ensemble ML approach can help us find the best model candidates while being sure that we are appropriately capturing the desired phenomenon with a greater degree of certainty.

Alternative iterative methods for model and parameter identification

Alternative algorithms for inferring model structures and parameter values include decision trees or random forests ^97–99, genetic or evolutionary algorithms^100–102, and gradient boosting^103,104. Essentially, these are iterative methods that allow a user to sample a wide range of conditions and decide which set of parameters or model structure makes the most sense for the data. The accuracy of the model is improved with each iteration, a model is decided, and ultimately the model candidates are tested or validated on an independent data set. Applications of such algorithms to date have shown potential for refining the process of ADME parameter estimation and integration into a larger PBPK model¹⁰⁵. However, all of these methods contain an inherent risk of overfitting. Even random forests, often considered to be among the most robust approaches, are still susceptible^106,107. This issue of overfitting can be addressed manually, through restricting a model to a strictly mechanistic system¹⁰⁸, or through the introduction of a penalty associated with increasing the size of the model (e.g., Least Absolute Shrinkage and Selection Operator (LASSO), marginal, or ridge regression with or without boosting)^109,110.

Sometimes the best model candidate is a minimal PBPK (mPBPK) model. mPBPK modeling is traditionally used in the scenario of many unknowns as a means of obtaining a simplified model that captures the primary variable of interest, often plasma concentration^9,111. Since the scope of the mPBPK model is more limited, the model structure and parameter values become far easier to learn. AI is invaluable for informing or deciding which elements are critical to a reduced system. When a model framework and parameter values are learned, decisions on the top model candidates are made based on reducing the error between a desired benchmark and the model prediction. Iterations of the model are then constructed based on error minimization, where parameters with the greatest sensitivity (and hence the greatest capacity to affect error) are the most critical components of the updated model.

In the best-case scenario, the proposed inferred model system can point to a potentially under-investigated mechanism of physiology, thus improving our mechanistic understanding. Regardless of whether the mechanism in the inferred model holds biologically, the benefits of a predictive model are invaluable for generating or validating difficult-to-obtain data with greater confidence.

Neural networks and large language models

Neural networks consist of layers of independent, interconnected nodes representing input, output, and a series of steps through which output is derived from the input^112–114. The sequence of events through which the model learns which outputs are associated with which inputs mimics associations formed by neurons firing in the brain¹¹⁴. During model training, correct associations are rewarded, while incorrect associations are penalized¹¹⁵. When multiple steps exist, as opposed to a single layer, between the input and output layers, the network is referred to as a deep neural network. The complexity of training multiple layers poses a model optimization tradeoff wherein a sufficient number of layers are needed to fully capture the problem at hand, but models with fewer layers are more reliably trained¹¹⁵. Traditionally, neural network models have been effective for classification and pattern recognition tasks. More recently, they have also been used to learn model structures in PK and other domains where there is insufficient data to fully inform a mechanistic model, for example, in extrapolating from sparse concentration-time profiles¹¹⁶.

Large language models (LLMs), a subclass of neural network-based work, have recently gained prominence with the advent of commercial tools such as ChatGPT, Gemini, Copilot, and others^117–119. LLMs are specifically optimized to learn patterns and make associations with language, in models where inputs and outputs consist of words and phrases, much like a human brain processes speech. In their current state, caution must be taken to avoid “hallucinations,” in which undiscerning LLMs report false statements as fact. However, they are valuable for summarizing information, parsing large data sets, sifting through disjointed reports of data, and even suggesting potential mechanisms for further investigation. These features contribute to the appeal of adopting LLMs for medical applications¹²⁰.

Hybrid modeling

The concept of hybrid modeling generally refers to integration of multiple modeling techniques, e.g., combining mechanistic models (where a system is well characterized) with ML models (where the system is poorly characterized), or multiple layers of ML models to most effectively capture complex processes. Hybrid models have been successfully used in many pharmacological applications. For example, Boolean network models underlying a system of ODEs have informed quantitative systems pharmacology (QSP) models as a means of screening and identifying targets¹²¹, as well as more generally accounting for underlying signaling processes throughout systems medicine^122,123. A deep learning model optimized through Bayesian methods has yielded drug concentration prediction results comparable to traditional NONMEM predictions¹²⁴.

Additional examples of successfully integrating ML/AI to advance PBPK modeling, often in combination with other modeling techniques, are discussed below.

Specific examples of applications of ML/AI in PBPK modeling and future potential

The idea of harnessing the fundamentals of ML to parameterize PBPK models, understand sources of variability, and address current challenges in PBPK modeling is gaining traction and has already been applied successfully in several systems. Recalling our IgG example, Garg and Balthasar used maximum likelihood estimation to fit the unknown parameters for IgG endosomal compartment uptake rate, fraction recycled, and the rate of recycling in their antibody model¹¹. They employed a normalized sensitivity analysis to reveal that the model predictions are most sensitive to IgG fraction recycled via FcRn. Based on the sensitivity of their model, they concluded that FcRn plays a larger role than previously thought in IgG distribution, in a tissue-specific manner. Krauss et al. employed MCMC to uncover population subgroups and sources of heterogeneity in response to pravastatin (Figure 2)⁷¹. By separating sources of variability into patient-specific parameters and drug-specific parameters, then examining the subpopulations of patients that resulted from their inferred parameter distributions, they concluded that variation in OATP1B1 transporter activity is responsible for inter-patient variability in pravastatin distribution. Both of these examples illustrate the role of learning aspects of a model system in facilitating a deeper understanding of the mechanisms at the molecular level and across patient populations.

Figure 2.

Concentration of pravastatin obtained from patient data (open shapes) and predicted from Bayes-MCMC PBPK model (solid lines) in (A) all patients and (B) representative patients highlighting inter-patient variability. Figure obtained from ref [71] (CC BY 2.0 DEED).

Our previous work implemented an LHS-PBPK framework to parameterize an 8-compartment PBPK model for PEGylated liposomes and proteins, in mice and humans^58,64. Our model predictions for concentration-time profile were in good agreement with the data for animals (Figure 3) as well as populations with and without anti-PEG antibodies (APA). Utilizing non-invasive PET/CT imaging over time, we were able to infer the parameters corresponding to organ-specific uptake and retention, with the model revealing that liver and splenic retention were significantly increased in animals with high levels of APA exhibiting accelerated blood clearance. Biologically, the most plausible explanation is sequestration of APA/drug immunocomplexes by liver sinusoidal endothelial cells (LSEC). In this instance, the learning aspects of the PBPK model for biodistribution of PEGylated drugs were instrumental in elucidating the role of APA in altered systemic clearance.

Figure 3.

Comparison between PBPK model predictions (turquoise line) vs. biodistribution data obtained by in vivo PET/CT imaging (black dots) in (A) a representative naïve mouse and (B) a representative APA+ mouse. Concentrations are normalized as % injected dose/g, where 1 = 100% ID/g. Figure reprinted from ref [64], with permission from Elsevier.

Recently, more attention has been given to ML as a means of integrating multi-omics data modalities in parameter estimation¹²⁵. A proposed “ML-PBPK” system by Li et al. boasted higher accuracy using learned physicochemical properties vs. in vitro data, supporting the combined approach¹²⁶. Their model was constructed based on a “bottom up” approach using the predicted human PK properties (uptake, permeability, and clearance) of 40 small molecule drugs. It yielded an Area Under the Curve (AUC), or total drug exposure, prediction accuracy of 62.5% vs. the in vitro AUC accuracy of 47.5%. This work underscores both the potential for making predictions of anticipated PK in humans strictly based on in silico results, and the necessity of further understanding sources of variability in the complex human system. It also highlights the utility of previously obtained PK data and the importance of database management, such that relevant model training data is available for ML-PBPK.

Paixão et al. used an artificial neural networks ensemble approach to predict tissue-to-blood partition coefficients (K_t:b) for a variety of compounds and tissue types, which were then fed into a PBPK framework ⁹⁵. They optimized their neural network structure for a selected set of molecular descriptors of these compounds, by accounting for redundancy in the descriptors and testing models with different numbers of layers and nodes. Their model yielded a partition coefficient prediction in strong agreement with observed in vitro and in vivo values for K_t:b in 13 tissue types in rats, as well as an approximation for the volume of distribution at steady state (Vss) for over 500 drugs in humans. The molecular descriptors, including pKa, molecular weight, lipophilicity, and others, together determined tissue distribution. The Vss prediction accuracy negatively correlated with the variability of the partition coefficients for each tissue, once again highlighting the importance of the complexity of modeling a human system. A high variability coefficient was interpreted as a drug being outside of the applicability domain, once again underscoring the importance of relevant training data. In this model, results were the least accurate for large molecule drugs, as the model was not sufficiently trained to handle drugs with these properties.

Mavroudis et al. employed ML to predict plasma exposure based on PK properties derived from the molecular structure of a new drug candidate (Figure 4)¹²⁷. Their work again suggests a need for greater understanding of model variability to maximize the accuracy of this approach. Namely, the model was more variable and less accurate when a variable primary clearance mechanism existed, which highlights the necessity of a comprehensive training set in determining accurate predictions. PK parameters have also successfully been estimated based on chemical structure by the ML algorithms of Miljković et al¹²⁸. and Murad et al¹²⁹. AI methods have also been increasingly proposed as a means of increasing efficiency for gathering robust, reliable data and learning ADME and toxicity based on QSAR, including ADMET-AI¹³⁰ and ADMETboost¹³¹ that leverage neural net and gradient boosting techniques. Such techniques seek to directly address the issue of limited and difficult-to-obtain data.

Figure 4.

Representation of observed plasma exposure vs. PBPK model predictions using CL and Vss parameters determined by ML. (A) Observed vs. predicted plasma exposure in a rat model. (B) Observed vs. predicted AUC at the terminal time point. (C) Observed vs. predicted maximum concentration (C_max). Figure obtained from ref [127] (CC BY 4.0 DEED).

An integrated ML and PBPK approach by Habiballah and Reisfeld highlighted a workflow in which crosstalk between learning and mechanistic PBPK can strengthen model predictions¹³². The model output was reported by the normalized summary pharmacokinetic metrics (SPKMs) C_max/dose (peak concentration), t_max (time of peak concentration), and AUC/dose. In this workflow, rather than an underlying ML prediction feeding into a PBPK model, the PBPK model itself was implemented to generate predictions for sets of drugs with specific properties. The PK properties were then calculated for sets of drugs with similar properties based on a learned model, as a means of reducing the complexity and computational burden of a full mechanistic PBPK model pipeline. Although predictions from the combined ML approach were in good agreement with the purely PBPK approach, at times both approaches yield predictions that were relatively different from experimental data (Figure 5). While overall promising, this underscores the need for fundamentally understanding or being able to learn the PBPK model structure for our drug delivery process.

Figure 5.

Representation of traditional PBPK (OpenCAT) predictions (blue circle), ML predictions (yellow triangle), and experimental data (bars), for C_max/dose, t_max, and AUC/dose. Figure obtained from ref [132] (CC BY 4.0 DEED).

Natural language processing (NLP), a class of methods that include LLMs, has recently been adapted to support PBPK analyses of new molecular entities (NMEs). Specifically, Hsu et al. implemented a custom deep learning model that allowed for a system of manual checks and inputs, providing additional training input as needed. Among their case studies, their interactive and iterative model approach allowed them to identify dosing strategies and PK parameter covariates based on information gleaned via NLP and compare to manual curation (Figure 6)¹³³. Such findings suggest that successfully leveraging NLP can allow one to broaden an initial literature search and expedite the process of defining, building, and implementing comprehensive PBPK models. Utilizing this more expansive approach to PBPK model development has the potential to increase the applicability of PBPK model predictions by improving efficiency and access to more comprehensive sources of data. In fact, their analyses of data extracted from the FDA website on the use of PBPK modeling in the evaluation of new molecular entity and biologic drugs provide further evidence of the increasing role of PBPK in the regulatory sphere and the utility of detecting adverse interactions based on broad AI-assisted surveys.

Figure 6.

Representation of covariates identified by NLP in PK models of large (blue) and small (yellow) molecule oncology drugs. Figure obtained from ref [133].

ALB, albumin; ALT, alanine transaminase; AP, alkaline phosphatase; AST, aspartate aminotransferase; BILI, bilirubin; BSA, body surface area; BWT, body weight; CRCL, creatinine clearance; ECOG, Eastern Cooperative Oncology Group performance status; FDA, US Food and Drug Administration; IGG, immunoglobulin G; PK, pharmacokinetic; PopPK, population pharmacokinetic; PPI, proton pump inhibitor.

There is also recent precedent for AI models to streamline delivery predictions for nanomedicines, in which drug delivery behavior is learned from the properties of the nanoparticles¹³⁴. This framework seeks to infer the delivery of a new nanomedicine to the tumor site by utilizing data from previous in vivo studies of nanomedicines, available from a Nano-Tumor Database¹⁸, rather than new in vivo studies. The time series for predicted tumor concentration from the AI-informed PBPK model, with parameters learned from the nanoparticle database, recapitulated previously published experimental data with high accuracy, thus potentially providing an alternative to animal studies as a screening method. Combining deep learning and ensemble models may further improve nanoparticle PK predictions by incorporating information across nanomedicine datasets where the data are limited, accounting more fully for features unique to the ADME of nanoparticles versus larger drugs¹³⁵. It is important to note, however, that unlike small molecules and even biologics, nanoparticle properties and stability may differ substantially due to subtle differences in technique or quality control in manufacturing that are rarely described, not to mention actual physicochemical differences among different nanoparticle systems. This in turn can greatly influences observed in vivo behavior, and thus potentially limit the predictive power of any strictly AI approach.

Recent improvements to PK predictions span both modeling and treatment modalities, as evidenced by the variety of techniques and applications in the following examples. Neural networks, response surface methodology, and PBPK have been combined in the development and analysis of rivaroxaban controlled-release tablets with low solubility¹³⁶. Specifically, a neural ordinary differential equations (neural-ODE) approach was able to predict PK measurements for new dosing regimens based on serum concentration levels from known regimens in humans receiving conjugated monoclonal antibody (the well-characterized trastuzumab emtansine) therapy, with greater accuracy than alternative models¹³⁷. An ML model for predicting PK profiles of intravenously administered compounds in rats yielded results comparable to traditional methods when analyzing the PK profiles of thousands of small molecules¹³⁸. An integrated AI-PBPK model has successfully predicted tissue distribution of over 600 oral and 71 intravenous drugs from the PK-DB database based on their physicochemical properties (enumerated as solubility, pKa values, crystal density, intrinsic dissolution rate, apparent permeability, protein unbound fraction, plasma clearance, and tissue partition coefficients for 15 organs), and proposed a method of leveraging allometric scaling to integrate data optimized across species¹³⁹. By integrating available data sources to make predictions, such approaches reduce the gap between in vitro studies, early in vivo work, and the clinical result which often does not agree with expected behaviors based on preclinical results¹⁴⁰.

Summary: Future directions of AI in PBPK modeling

Given the high costs of preclinical and early clinical development, advancing the correct drug candidate at the right doses is paramount, which in turn underscores the importance of accurately predicting a drug’s concentration profile over time in the body. Currently, PK and biodistributions are most frequently determined very late in the drug discovery process, only after a candidate has been selected. Indeed, PK are often measured and PK modeling performed as part of toxicokinetics assessments in the GLP toxicology studies necessary to enter human studies. In principle, a more accurate understanding of PK/biodistribution properties via modeling should enable researchers to eliminate, earlier in the drug discovery and development process, drug candidates with undesirable PK/biodistribution profiles that make them unlikely to be efficacious or safe. This in turn not only reduces unnecessary sacrifice of lives from animal studies, but by extension can enable more cost-effective and faster drug discovery and development. As such, we believe it is only a matter of time before PBPK modeling is firmly entrenched as part of in silico drug discovery.

Early adaptation of AI and ML techniques to PBPK modeling is already increasing the predictive power and confidence in PBPK models, while enhancing our understanding of the sources of uncertainty and reducing them where possible. To date, most applications of ML that are currently implemented in PBPK are used to estimate parameters or parameter ranges. While there is still room to develop in this area, implementing ML/AI in the context of model selection and model learning remains an area rich in opportunities for growth in the PBPK field. In parallel, advances in database management and web scraping technologies can improve our ability to more efficiently and/or more accurately obtain relevant ADME parameters. These trends have the potential to increase the role of PBPK in every step of the drug development process, from early drug discovery to formulation optimization to investigational new drug (IND) enabling studies to clinical development. Doing so could replace iterations of costly experimentation with iterations of a learned model, thereby reducing not only time and costs but also potentially improving both efficiency and accuracy throughout the drug discovery and development process.

We believe there is room to incorporate PBPK modeling at every stage of the drug discovery and development pipeline. ML/AI techniques should enable us to increasingly adopt sophisticated PBPK models even with only partial understanding of the PK parameters. For example, when targets are identified as part of the in silico drug discovery process, the algorithmic framework could be expanded at this stage to screen or test other critical aspects of drug design, such as anticipated delivery modalities or off-target interactions. Implementing a PBPK system in this context could inform the earliest phases of drug design, drug formulation, or engineering of drug carrier systems. As the drug design process continues, incorporating AI in a multiscale PBPK framework has the potential to become an invaluable tool for not only predicting where a drug is in the body, but also informing how we can best design a drug with the desired biodistribution pattern, as well as the most sensitive time points to sample in animal and human studies. Integrating such a model into a PD system would, in turn, both predict the outcome of a drug and inform the optimal design to maximize our ability to achieve that outcome. Over time, if PBPK predictions prove to be sufficiently accurate, it may one day take on an increasing role in informing the regulatory approval process¹⁴¹.