Challenging Traditional ADME Assumptions for Physiologically Based Pharmacokinetic Models for Intravenous Administration of Iron–Carbohydrate Nanomedicines: Potential Utility of Gold Nanoparticle Models as a Roadmap

Open Access
15.08.2025
Review Article

Erschienen in:

Verfasst von: Amy Barton Alston; Zhoumeng Lin; Heather Herd Gustafson; Beat Flühmann; Reinaldo Digigow; Vanesa Ayala-Nunez; Stephan Schmidt
Erschienen in: Clinical Pharmacokinetics | Ausgabe 10/2025

Abstract

Intravenous iron–carbohydrate complexes are a class of nanomedicines that are widely used globally to treat iron deficiency and iron deficiency anemia associated with a wide spectrum of disease states. Despite being widely used in clinical practice for more than seven decades, the understanding of their in vivo disposition including tissue biodistribution and kinetics of the nanoparticle degradation at the cellular level is not well-understood. Moreover, the critical quality attributes that influence in vivo pharmacokinetics have not been fully defined. In particular, the carbohydrate moiety plays an influential role in how the nanoparticulate iron–carbohydrate complex interacts with the biological system. Developing a physiologically based pharmacokinetic (PBPK) model would facilitate a deeper understating of the key nanomedicine attributes that predict in vivo performance. Because endogenous iron metabolism complicates pharmacokinetic modeling for this complex class of drugs, models of gold nanoparticles may provide a substantive roadmap to begin to build a viable PBPK model for iron–carbohydrate nanomedicines. In the future, PBPK models that integrate recent mechanistic data regarding tissue biodistribution and intracellular iron kinetics for parameterization have the potential to improve manufacturing quality and clinical use of these complex drugs.

Key Points

Iron–carbohydrate nanomedicines exhibit complex in vivo disposition, and pharmacokinetic modeling is complicated by underlying endogenous iron metabolism.

Gold nanoparticles could provide an informative roadmap for pharmacokinetic modeling of iron–carbohydrate nanomedicines.

Leveraging existing relevant modeling of gold nanoparticles and mechanistic data from the iron–carbohydrate nanomedicine that can be parameterized could generate PBPK models that optimize manufacturing quality and dosing for these widely used medications.

1 Introduction

Nanomedicines are generally engineered to circumvent pharmacokinetic (PK) challenges associated with some small molecule drugs. These challenges may be attributed to inherent limitations from unacceptable toxicity profiles, poor target tissue penetration limiting their efficacy potential, or their half-lives being too short to adequately furnish the desired pharmacologic effect [1, 2]. Drug products at the nanoscale exhibit vastly different pharmacokinetic profiles than small molecule drugs and every aspect of the PK profile is affected by the properties of the nanoparticle. Because of the complexity of biodisposition of nanomedicines, many PK parameters have not been fully established for nanoengineered drug products, as an inherent challenge exists in measuring both the free and nanoparticle-bound drug [3‐5]. This concept is notably important for tissue biodistribution, which cannot always be reliably extrapolated from serum PK profiles [6].

One therapeutic area that has benefited greatly from nanotechnology is iron deficiency. Iron deficiency is a ubiquitous global health problem affecting more than 2 billion people worldwide. Etiologies of iron deficiency and iron deficiency anemia are diverse and affect an expansive array of patients, including people with a myriad chronic illnesses (e.g., cancer, chronic kidney disease, and rheumatologic disorders), women across the age continuum (e.g., menstrual and other gynecologic blood losses), as well as people who experience blood loss during traumatic injury or surgery. Intravenous iron products are colloidal suspensions of nanoparticles that broadly consist of a complex of polynuclear ferric oxyhydroxide cores with a variety of heterogeneous carbohydrate ligands to ensure that rapid release of iron in plasma does not occur. The development of iron–carbohydrate nanoparticles was prompted by the observation that the rapid dissolution of iron salts or ferric oxyhydroxide products in plasma was associated with deleterious, and potentially fatal, adverse effects including hypotension and cardiovascular collapse [7]. These nanomedicines have been engineered to deliver iron safely to the mononuclear phagocytic system (MPS) where the iron is stored and then mobilized for delivery to serum transferrin to the requisite tissue compartment (Fig. 1). The carbohydrate moiety plays an influential role in how the nanoparticulate iron–carbohydrate complex interacts with the biological system. Ultimately, it is the entire complex that furnishes the pharmacological effect at the target tissue site. The physical characteristics, such as particle size, size distribution, surface structure, or morphology, are directly influenced by the carbohydrate moiety of the nanoparticles and dictate the PK of the individual iron–carbohydrates with regard to absorption (i.e., uptake into the MPS and release of iron from the nanoparticle), distribution, metabolism, and excretion. Therefore, the physicochemical characteristics of each individual iron–carbohydrate nanoparticle product dictate the PK and pharmacodynamic profiles that are unique to each intravenous (IV) iron product.

Fig. 1

Proposed 3D physical structure of two iron–carbohydrate nanoparticles, ferric carboxymaltose and iron sucrose (from [17]). Brown circles: iron cores; blue dotted line: localized carboxymaltose ligand; green dots: diffusely bound sucrose. Red ball-and-stick image denotes applicable ferric oxyhydroxide crystal structures. Orthogonal characterization employing techniques such as X-ray diffraction (XRD), cryogenic scanning transmission electron microscopy (cryo-STEM), small-angle X-ray scattering (SAXS), and small-angle neutron scattering (SANS) describe ferric carboxymaltose (FCM) as large prolate spheroidal clusters made up of several single NPs, small prolate spheroidal clusters made up of two single NPs, and free single NPs. Iron sucrose (IS) is described as prolate spheroidal clusters made up of single NPs, and a free, single, diffuse and dynamic layer of sucrose surrounding the clusters and/or single NPs

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Challenges related to biorelevant linkage between tissue biodistribution (where the pharmacologic activity occurs) and serum concentrations of both free and nanoparticle bound drug pose a twofold, unique challenge for iron–carbohydrate nanomedicines. First, there is no validated, widely available assay to measure the plasma concentration of intact iron–carbohydrate nanoparticle [8]. This is a substantive problem because of background endogenous iron in the biological system, which exists as multiple, dynamic iron species (e.g., iron that is transiently weakly bound to citrate and/or phosphate), and iron in plasma is also bound to several proteins (transferrin and to a lesser extent, serum ferritin) (Table 1) [9]. Thus, the precise profile of the intact iron–carbohydrate drug cannot be determined, necessitating several facets of estimation to produce a PK profile for drug bound iron. This challenge can also extend to lack of an existing assay that can distinguish iron derived from an iron–carbohydrate nanoparticle source versus a dietary source. Secondly, iron–carbohydrate nanomedicines are rapidly cleared by phagocytes by yet-unknown uptake mechanisms and then delivered predominantly to the target tissues: the liver, followed by the spleen, where they are biodegraded (metabolized) [10, 11]. Iron is subsequently mobilized on the basis of the individual patient’s homeostatic needs via normal iron transporters. However, this can be markedly impacted by underlying inflammatory conditions which induce hepcidin production [12]. Hepcidin is considered a master regulator of iron homeostasis and reduces ferroportin expression, which sequesters iron within the MPS. Additionally, there may be changes in homeostatic feedback loops with cell exposure to large amounts of nanoparticle-derived iron (e.g., increased ferroportin expression) or independent effects of cytokine activation [12, 13]. A PK study in healthy, anemic people showed that plasma hepcidin concentrations increased after administration of three different iron carbohydrate nanomedicines [14]. The area under the plasma concentration–time curve values were similar among the products but the maximal plasma concentration (C_max) values differed. The C_max for iron sucrose, which has a more diffuse carbohydrate ligand, appeared at 24 h, while the C_max for ferric carboxymaltose with a more stable, thick carbohydrate ligand demonstrated a C_max at 48 h. Therefore, serum PK profiles of total serum iron or iron bound to transferrin do not adequately inform the rate and extent of iron availability and transport to the target tissues, where the iron–carbohydrate nanomedicines furnish their pharmacologic effect. The limited utility of plasma PK profiles for nanomedicines to inform tissue biodistribution and, ultimately, their pharmacodynamic profile is not unique to iron–carbohydrate drug products and aligns with a seminal review published nearly a decade ago by Moss and Siccardi, which states “The pharmacodynamics of nanoparticles is strictly dependent on the penetration of nanoparticles in tissues and the interaction with the therapeutic targets” [15]. Because of the challenge of quantitative measurement of tissue biodistribution in vivo, parameterization for application to physiologically based pharmacokinetic (PBPK) modeling requires alternative approaches for computational models of iron–carbohydrate nanomedicines. This scoping review will discuss the physical structure of iron–carbohydrate nanoparticles and the biorelevant considerations of these features on in vivo PK profiles. Potential approaches to PBPK modeling will be discussed leveraging gold nanoparticle models as a potential roadmap.

Table 1

Iron species in human physiology

Iron species	Iron valence	Location	Function
Transferrin-bound iron (TBI)	Fe³⁺	Serum	Transport
Ferritin (Serum)	Fe³⁺	Serum	Surrogate marker for storage
Ferritin (Tissue)	Fe³⁺	Intracellular (mainly liver, spleen, muscles, bone marrow)	Storage
Hemosiderin	Fe³⁺	Intracellular (mainly liver, spleen, muscles, bone marrow)	Deep storage
Hemoglobin	Fe²⁺	Erythrocytes	Oxygen transport
Labile iron	Fe³⁺/Fe²⁺		May contribute to oxidative stress
Non-transferrin-bound iron (NTBI)	Fe³⁺	Serum	Intermediate/transitory state in metabolism
Labile iron pool (LIP)	Fe²⁺	Cytosol	May contribute to oxidative stress

2 Physical Structure of Iron–Carbohydrate Nanoparticles

Iron–carbohydrate nanoparticles consist of polynuclear ferric oxyhydroxide cores that vary in crystallinity structure and are surrounded by carbohydrate ligands. These nanoparticles differ in their particle size, particle size distribution, molecular weight, surface charge, and chemical composition of the carbohydrate ligands (Table 2) [16]. Therefore, multiple orthogonal methods are required to provide an adequate representation of the three-dimensional (3D) physical structure of iron–carbohydrate nanoparticles (Table 3). It should be noted that there is still a paucity of data evaluating the structure of iron–carbohydrate complexes at the nano–bio interface, especially with regard to potential plasma protein interactions to describe the complex protein corona [17]. However, characterization of the interaction of iron–carbohydrate nanoparticles with specific plasma proteins such as albumin and fibrinogen has recently been published, and data are evolving in this area [17].

Table 2.

Physicochemical characteristics of iron–carbohydrate complexes (adapted from [71])

Product	Molecular weight (kDa)	Particle size (nm) [21]	Zeta potential (mV) [21]	Crystalline structure
Iron sucrose	34–60 [72, 73]	8.3 (PDI 0.192)	pH 7.43: −26.20 pH 11.03 *: −28.15	Two-line ferrihydrite [21] Ferrihydrite and lepidocrocite [74] Akageneite [75]
Sodium ferric gluconate	289–440 [76]	8.6 (PDI 0.244)	pH 7.4: −29.70 pH 8.36 *: −29.10	Two-line ferrihydrite [21] Ferrihydrite and lepidocrocite [74] Akaganeite [75]
Iron dextran	165 [77]	12.2 (PDI 0.149)	pH 6.4 *: −15.30 pH 7.31: −17.25	Akageneite [21, 74]
Ferric derisomaltose	155 [78]	9.9 (PDI 0.182)	pH 6.3 *: −22.0 pH 7.35: −21.05	Akaganeite [21, 74, 79]
Ferric carboxymaltose	≈150 [80]	23.1 (PDI 0.07)	pH 5.36: 3.68 pH 7.26: −8.52	Akaganeite [21, 74, 79]
Ferumoxytol	750 [81]	23.6 (PDI 0.143)	pH 6.6: −43.20 pH 7.36: −30.55	Magnetite/maghemite [21] Magnetite [74] Maghemite [79]

*Not adjusted for pH

Table 3

Orthogonal methods used to determine the physical structure of iron–carbohydrate nanoparticles (adapted from [16])

Analytical technique	Iron–carbohydrate particle size	Iron–carbohydrate particle morphology	Iron core particle size	Iron core morphology/crystallinity	Carbohydrate ligand
DLS	X [82]
Cryo-(S)TEM	X [18, 19]	X	X	X
XRD				X [16, 20]
AFM	X [79]	X
XANES				X [79]
Size exclusion	X [21]
Mössbauer			X [83]	X (crystallinity) [79]
SAXS			X [84‐87]
SANS	X [88]		X [89]		X (thickness) [89, 90]
Zeta potential					X[21]

DLS dynamic light scattering, Cryo-(S)TEM cryogenic (scanning) transmission electron microscopy, XRD X-ray diffraction, AFM atomic force microscopy, XANES X-ray absorption near edge spectroscopy, SAXS small-angle X-ray scattering, SANS small-angle neutron scattering

Characterization of the iron core can be achieved using different techniques, such as cryogenic transmission electron microscopy (cryo-TEM), cryogenic scanning transmission electron microscopy (cryo-STEM), atomic force microscopy, or X-ray diffraction. It should be noted that multiple techniques should be utilized to generate the multiple vantage points of the structure to better understand their structure–function relationship in vivo. Generally, the iron cores are in the range of 2 nm in size, and the hydrodynamic diameter of the whole particles determined by dynamic light scattering (DLS) can range between 8 and 30 nm [17‐21]. The carbohydrate ligands of these nanoparticles remain difficult to fully characterize [17]. Zeta potential measures the surface charge of the carbohydrate ligand and is the most common parameter used to characterize the surface of iron–carbohydrate nanoparticles. This parameter is important for the nanoparticle’s in vivo behavior because it measures the collective charge of the surface of the nanoparticle, which influences colloidal stability as well as the interaction with plasma proteins and subsequent cell uptake into the key pharmacologic tissue sites of action [21]. Analytical methods used to characterize the intact iron–carbohydrate nanoparticle have advanced in recent years. DLS is by far the most widely validated and utilized method to characterize the particle size of the whole, intact nanoparticle [22]. The readout of this technique provides both the hydrodynamic size (z-average) and particle size distribution (polydispersity index (PDI)) by measuring fluctuations in scattered light intensity and using the Stokes–Einstein equation to estimate the hydrodynamic diameter. However, it should be noted that DLS requires dilution of the iron–carbohydrate preparation to ensure adequate and accurate signals from the light scattering function, which may not represent the physical structure and interaction of the nanoparticles in their pristine state before injection [22, 23]. One drawback of utilizing DLS is the challenge of conducting in situ analysis that could better describe the nanoparticle disposition in plasma matrices due to multiple peaks from serum proteins. Additionally, there can be a significant bias in the particle size distribution, as larger particles or proteins bias the detection profile with this technique and differences in particle size subpopulations may affect biodistribution [22]. Recently, newer, orthogonal methods have been applied to characterize iron–carbohydrate complexes, adding more information to the elucidation of their 3D structure in situ as well as their interactions with plasma proteins (e.g., protein corona) [17]. A study by Krupnik et al. modeled the intact nanostructure and the individual components of iron sucrose (IS) and ferric carboxymaltose (FCM) using multiple orthogonal techniques [17]. Importantly, the study approach combined morphological information from cryo-STEM with high-statistics data from small-angle X-ray scattering (SAXS) to characterize the iron core and complement these data with small-angle neutron scattering (SANS) to elucidate the carbohydrate ligand morphology. Differences were observed in the nanostructure between IS and FCM, which were apparent in their cluster formation, crystallinity, and carbohydrate ligand morphology. The observed cluster formation was smaller for iron sucrose (~8.0 nm in size), which also formed aggregates, compared with FCM, which showed both small (~5.0 nm in size) and large (~17.0 nm in size) cluster formation (Fig. 1). Differences were also demonstrated in serum protein interactions between the two iron–carbohydrate complexes. The structural model showed that IS interacted with both human serum albumin and fibrinogen, while FCM only showed interaction with fibrinogen. The authors hypothesized that the difference in carbohydrate ligand morphology plays a key role in their protein interaction profiles. Differences among iron–carbohydrate complexes in their serum protein interactions or protein corona formation may affect how these complexes interact in the biological environment. FCM may initially be recognized as a bare cluster with a carbohydrate surface, while IS may rapidly interact with serum proteins and be surveilled by phagocytes as a nanoparticle–protein cluster. This could explain differences in bioresponses, such as changes in nanoparticle clearance kinetics from serum, macrophage uptake, and release rates of bioactive iron from the nanoparticle after distribution to the liver and spleen. The structure of iron–carbohydrate nanoparticles seems to be more complex and dynamic than previously observed with more standard physicochemical characterization techniques (i.e., DLS). Moreover, preliminary data reveal that there does appear to be important interactions with plasma proteins that collectively drive the rate and extent of tissue distribution, which in turn affects the PK and pharmacodynamic profiles for each individual product [17].

3 Absorption, Distribution, Metabolism, and Excretion (ADME) Considerations for Iron–Carbohydrate Complexes in the Context of PBPK Models

3.1 Absorption

Traditional PK approaches for small molecule drugs follow the well-established paradigm that bioavailability is 100% following intravenous injection. However, this assumption must be fundamentally challenged when considering in vivo behavior of nanomedicines. As described previously, iron–carbohydrate nanoparticles must be delivered to the MPS to be biodegraded and metabolized to allow iron to be released from the nanoparticle and then incorporated into normal iron storage (tissue ferritin). The rate and extent of iron uptake and release have not been established in any in vitro model, and any validated model would need to have the capability to discern iron kinetics in the context of elevated hepcidin concentrations. A study funded by the US Food and Drug Administration attempted to develop an in vitro to in vivo correlation (IVIVC) model based on labile iron release from iron–carbohydrate nanoparticles using a chelatable iron high-performance liquid chromatography (HPLC) assay [24] and correlating the release profile with plasma labile iron PK profiles in rats [25]. Labile catalytic iron represents only a very small fraction (reported to be 0.07–1.4% of the administered dose depending on the iron–carbohydrate product) of potentially bioavailable iron from iron–carbohydrate complexes [9, 26]. A point-to-point IVIVC could not be established using this approach [25]. This is likely due to the limited contribution of labile iron to the overall PK profile of iron–carbohydrate nanoparticles, given that this small amount of iron dissociated from the nanoparticles occurs before metabolism in the liver and spleen [14]. The rate and extent of liver and spleen macrophage uptake, nanoparticle metabolism in vivo, and subsequent rate and extent of iron exported from these tissue compartments remain poorly characterized, especially in the context of chronic diseases associated with chronic inflammation and hepcidin upregulation [27].

3.2 Distribution

The bioavailability of iron from the iron–carbohydrate complexes depends on cellular-level metabolism, making tissue distribution a critical factor in understanding and modeling the in vivo behavior of iron–carbohydrate complexes in both health and diseased conditions. Therefore, refining and validating in vitro uptake methodologies would greatly improve the predictive performance of parameters generated from these experiments [28]. The lack of ferromagnetic properties of the commercially available intravenous iron nanomedicines limits the development of viable model parameters. While several studies have employed radiolabeling methods [29] to provide insights into the rate and extent of iron–carbohydrate nanomedicines biodisposition (pathway outlined in Fig. 2), little is known about how the labeling procedure may affect the final physicochemical properties of the iron–carbohydrate complex.

Fig. 2

Proposed biodisposition pathway for iron–carbohydrate nanoparticles (from [71])

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In an early study from 1969 using iron dextran, Henderson and Hillman administered radiolabeled (⁵⁹Fe) iron dextran to 25 anemic subjects with absent bone marrow iron staining [30]. The total dose of iron ranged from 100 mg to 2 g, and a second bone marrow aspirate was obtained between 2 and 5 days postadministration. During the follow-up period, up to 14 days, frequent sampling was performed to measure radioactivity in plasma and whole blood (red blood cells, RBCs). The authors proposed a calculation to estimate iron distribution to MPS storage:

$${\text{MPS storage }} = {\text{ Total infused iron }}{-} \, \left( {{\text{Iron in plasma at bone marrow aspiration }} + {\text{ Iron in RBCs}}} \right)$$

A plot of bone marrow iron grading versus calculated MPS stores showed an apparent positive correlation, emphasizing the role of MPS distribution in mobilizing bioavailable iron for transport to the bone marrow. Red cell utilization was determined by measuring whole blood radioactivity 10–14 days post-iron dextran infusion. In otherwise healthy anemic patients, red blood cell uptake of the administered iron ranged from 89 to 96%. By contrast, patients who were described by the authors to have a “complicating illness of an inflammatory nature” had far lower red blood cell uptake of radioactive iron, ranging from 26 to 86%. These data underscore substantial interpatient variability that must be accounted for in any models of iron–carbohydrate complex administration.

In 1999, Beshara et al. evaluated the distribution of tracer labeled (⁵²Fe/⁵⁹Fe) iron sucrose complex in six patients in real time up to 8.3 h using positive emission tomography (PET). Rapid uptake was observed in the liver and spleen within 60 and 20 min of administration, respectively. Isotope uptake in the liver and spleen was followed by a slow, steady decline over the observation period. In the bone marrow, rapid uptake was observed during the initial 100 min post-iron administration, followed by a continuous rise in uptake until the last measured timepoint. In four of the six patients, bone marrow uptake exceeded that of the liver. However, the two remaining patients, who had chronic inflammatory conditions—diabetic nephropathy and rheumatoid arthritis—exhibited a different uptake pattern, likely due to hepcidin upregulation and iron-restricted erythropoiesis. These findings highlight the primary organs involved in iron distribution and underscore intersubject variability, which may be influenced by inflammation and mononuclear phagocyte system (MPS) blockade of iron release [31‐33].

The limitations of detailed tissue biodistribution studies in humans prompted a series of systematic biodistribution studies in an anemic male rat model [34]. The studies were conducted in three phases; (1) establishment of a diet-induced anemic rat model, (2) evaluation of iron biodistribution in healthy and anemic rats receiving a control vehicle (normal saline) and anemic rats receiving 30 mg/kg of ferric carboxymaltose, and, finally, (3) comparative biodistribution analysis in anemic rats treated with 30 mg/kg of iron sucrose, ferric carboxymaltose, iron isomaltoside 1000, and iron dextran. Plasma samples were collected to establish a serum iron-time concentration profile, and tissue samples were harvested at days 3, 8, and 15 post-iron–carbohydrate complex administration. Iron deposition was determined by inductively coupled mass spectrometry (ICP-MS) and reported as mg iron/g tissue. Pharmacokinetic analysis revealed that the maximal serum iron concentration (C_max) and area under the concentration–time curve (AUC 0 to 48 h) were comparable across all iron–carbohydrate complexes, except for ferric carboxymaltose, which exhibited the lowest serum iron AUC. Despite similar serum iron PK profiles, each iron–carbohydrate complex produced a unique biodistribution pattern. Ferric carboxymaltose resulted in the highest initial liver concentrations, while iron dextran led to the greatest spleen deposition. Moreover, differences in iron trafficking and storage (i.e., amount of tissue ferritin present) were evident amount the iron–carbohydrate complexes. These findings underscore the limitations of conventional PK parameters and noncompartmental modeling techniques in differentiating the biodistribution profiles of structurally heterogeneous iron–carbohydrate complexes.

3.3 Metabolism

Iron–carbohydrate complexes do not exhibit traditional drug–enzyme interactions that lead to water-soluble, excretable metabolites. In addition to continuous background endogenous iron metabolism, this poses another relevant challenge to developing PBPK models, as these types of interactions have been extensively modeled and can be relatively easily applied to new models. The exact mechanism of metabolism of the iron–carbohydrate complexes has not been extensively studied. It is also important to note that normal iron metabolism, in the absence of administration of an iron–carbohydrate complex, remains poorly understood when inflammation or other interfering conditions are present [35]. Recent work by Ayala-Nunez et al. has shown that after uptake of iron–carbohydrate nanoparticles, the rate at which the iron nanoparticles enter the lysosome and then form endolysosomes differs between drug products [36]. Iron sucrose appears to be rapidly incorporated into lysosomes and is then degraded in endolysosmes. By contrast, ferric carboxymaltose appears to accumulate slowly forming large endosomes before forming endolysomes. This also seems to translate into slower appearance of intracellular ferritin indicating delayed mobilization of iron from the nanoparticle compared with iron sucrose.

3.4 Excretion

Iron is typically highly conserved, and only limited excretion occurs in healthy patients, mainly by shedding of the gastrointestinal epithelium, gastrointestinal blood loss, menstrual blood losses, sweating, and exfoliation of skin cells [32, 37]. Iron is also highly recycled mainly via erythrophagocytosis in the spleen and, to a lesser extent, the liver and bone marrow [38]. Thus, while excretion is not an important factor in drug elimination for iron–carbohydrate products, their relatively small size may influence deposition in the kidney.

The in vivo biodisposition of iron–carbohydrate nanomedicines is complex and this translates to formidable challenges in characterizing their PK profile in vivo [6, 39]. In contrast to superparamagnetic iron oxide nanoparticles (SPIONs), iron–carbohydrate nanomedicines used to treat iron deficiency and iron deficiency anemia clinically are either nonmagnetic or very weakly ferromagnetic, which greatly limits the availability of techniques to quantitate nanoparticle-bound iron in vivo directly [40]. Importantly, there is limited mechanistic understanding of how the nanoparticles are taken up by phagocytic cells and then delivered and stored in the MPS (i.e., the liver and spleen). These macrophages exhibit high thresholds to process and store large amounts of iron (in ferritin and to a lesser extent hemosiderin) without evidence of ferroptosis [41]. Silva et al. described a translational approach to predicting carbohydrate-coated SPION accumulation in vivo using a PBPK model [40]. The authors conducted in vitro macrophage uptake experiments in murine and primary human macrophage cells to determine the rate and extent of SPION uptake to ultimately parameterize these for inclusion in the final PBPK model.

4 Development of PBPK Models for Iron–Carbohydrate Nanoparticles: Challenges and Opportunities

PBPK modeling is a computational modeling and simulation process that describes the absorption, distribution, metabolism, and excretion (ADME) of chemicals, nanoparticles, and/or their metabolites in the body on the basis of the interrelationships among key physiological, biochemical, and physicochemical properties using mathematical equations [42, 43]. PBPK models have been commonly used in human health risk assessment of environmental chemicals, animal-derived food safety assessment, and therapeutic optimization of drugs, as well as in the discovery, development, and approval of new drugs, especially small molecular drugs and biologics [44‐47]. Many PBPK models have also been developed for a variety of nanoparticles and have been shown to be useful in supporting nanoparticle risk assessment and improving our understanding of the ADME properties of nanoparticles [48, 49]. However, PBPK models have not been reported to support regulatory approvals of nanomedicines to date. Unlike small molecular drugs for which PBPK modeling methodology is well established, the methodology for PBPK modeling of nanomedicines is still developing. Nevertheless, there has been substantial progress in the PBPK modeling of nanoparticles. The following discussion will summarize what we have learned from PBPK modeling of small molecules and other nanoparticles that could facilitate development of PBPK models for iron–carbohydrate nanoparticles in the future.

It is well-recognized that the ADME properties of small molecular drugs and nanoparticles are quite different. As such, the PBPK modeling strategies for small molecular drugs and nanoparticles are also different. Table 4 lists the major differences between small molecules and nanoparticles in the ADME properties and PBPK modeling methods. Knowing these differences is important, as it will help in application of the most appropriate methodology to develop PBPK models for nanoparticles, including iron–carbohydrate nanoparticles.

Table 4

Comparisons in pharmacokinetic properties and physiologically based pharmacokinetic (PBPK) modeling between small molecules and nanoparticles

PBPK modeling considerations	Small molecules	Nanoparticles
Dose metrics and unit	In mass per unit volume, such as mg/L or mM/L for concentration of a chemical in plasma or mg/kg in tissues	Usually, the same as small molecules in mass per unit volume [91], but some studies showed that the dose metrics of particle number or surface area may be more appropriate for certain toxicity endpoints, such as lung inflammation [92‐94]
Absorption	Approaches to simulate extravascular absorption for small molecules are well established. Depending on the administration route and availability of data, it could be a simple first-order linear absorption or a more complex mechanistic model, such as the advanced compartmental absorption and transit (ACAT) model for oral absorption.	Approaches to simulate extravascular absorption of NPs remain to be established. In general, the absorption of NPs from extravascular routes is very low owing to the size of the particle. This makes it difficult to collect time-dependent kinetic data to build a PBPK model for extravascular routes. Currently most PBPK models for NPs are only for IV route, with a few that also include oral route, such as gold nanoparticles [52] and titanium dioxide nanoparticles [95]
Model compartment structure	Both perfusion-limited and diffusion-limited model structures are appropriate depending on the physicochemical properties of the chemical (e.g., molecular weight, lipophilicity, and hydrophilicity)	Most existing PBPK models for NPs are based on a permeability-limited model structure, such as gold nanoparticles [52] and superparamagnetic iron oxide nanoparticles coated by gold and conjugated with PEG [61]. Most of these models divided an organ into three subcompartments, including vascular space, phagocytic cells that actively uptake NPs, and rest of the organs.
Circulation through body	For many small molecules, systemic distribution occurs through the blood circulatory system	Trafficking through the lymphatic system may also occur and dictate the structure of the PBPK model used. Note that for PBPK modeling of monoclonal antibodies, it is well accepted that the lymphatic system plays an important role in tissue distribution and should be included in a PBPK model [96]. For NPs, many existing PBPK models for NPs did not include lymphatic systems, but a few did [49, 65, 97].
Plasma protein binding	Small molecules can undergo nonspecific protein binding (e.g., plasma albumin) by an equilibrium process. This can be described as a saturable process (e.g., association rate constant, dissociation rate constant, and maximal binding capacity). Alternatively, this can be simply described using a plasma protein binding percentage assuming this percentage remains the same across a wide dose range, which can be supported if experimental data are available.	NPs may associate with multiple proteins and other macromolecules in a dynamic fashion, sensitive to the environment, to form a biocorona that could be a primary determinant of biodistribution and elimination. Protein coronas could be “hard” or “soft” depending on the affinity and interaction between NPs and proteins. Approaches to incorporate biocorona formation kinetics into a PBPK model for NPs have not been established, but mathematical models describing the in vitro kinetics of nanoparticle-protein corona formation have been published [98, 99]
Cellular uptake	In most cases, cellular uptake occurs by either diffusion down a concentration gradient or by classic molecular transporter systems (organic acid transporter system, p-glycoprotein, etc.) that are well described using saturable but reversible models (e.g., Michaelis-Menten)	Cellular uptake is via capacity-limited vesicular transport systems with charge and size specificity (e.g., phagocytosis, micro- and macro-pinocytosis, and membrane rafts) [100]. Release of NPs from cells via exocytosis should be considered when simulating the cellular uptake and release kinetics. Uptake and release kinetics in endocytic cells (or phagocytic cells as a generic term) have been considered in most existing PBPK models for various nanoparticles [49]
Tissue trapping	Small molecules which are weak acids or bases get ion-trapped in tissues with different pH, as only the noncharged moiety can diffuse across the membrane. This process can be calculated using the Henderson–Hasselbalch equation	NPs have colloidal properties that result in aggregation or agglomeration depending upon local microenvironment (pH and ionic strength). NPs may change size and surface properties when they enter tissue sites or cellular compartments (e.g., lysosomes), which may influence their movement, often trapping on the side of membrane promoting aggregation [101, 102]
First-pass effects	The pathway of absorption of a small molecule chemical into the body may have a major impact on its subsequent deposition by first-pass hepatic metabolism	If an absorbed NP forms a tight association with a biomolecule (e.g., protein and surfactant) in the process of absorption, its subsequent deposition could be changed.
Metabolism or biotransformation	Common for small molecule chemicals and are mediated by Phase 1 and/or Phase 2 enzymes. Metabolism is usually simulated using the Michaelis–Menten equation and can be measured using in vitro systems and then extrapolated to in vivo using physiological scaling factors. If experimental data are not available, metabolism can also be described using a simple first-order equation provided that the drug doses are within the linear kinetic range	Many “hard” NPs (e.g., metal and carbon) are relatively inert and often too large to be degraded or metabolized by enzymes. However, several metal NPs, such as silver NPs, can be metabolized to become silver ions.[95] For organic NPs, especially polymers with a functional group on the surface, the functional group may be degraded by enzymatic process.[49] Existing PBPK models for NPs only simulate the pharmacokinetics of the NP itself. The mechanism of metabolism of NPs remains to be investigated, and the approaches to simulate NP metabolism remain to be established.
Excretion	Mainly through urinary, fecal, and biliary excretion routes, and can be described using either first-order linear progress or saturable process depending on the mechanism and availability of data	Excretion is generally slow for NPs due to long retention time in tissues, especially in tissues of the RES system (e.g., liver, spleen, lungs, and kidneys) and the size limitation. Usually, small NPs (≤5–6 nm) are excreted through the kidney, and larger NPs are mainly excreted via biliary pathway [103, 104]
IVIVE	IVIVE approaches are well established for small molecules. It is common to determine PBPK parameters in vitro and then extrapolate to a whole-body PBPK model using physiological scaling factors. The latest PBPK guideline from OECD provides details on how to develop and evaluate/validate a PBPK model based on in silico and in vitro data only	Most published PBPK models for NPs were built on the basis of in vivo pharmacokinetic data. One recent study demonstrated it was possible to develop a PBPK model for NPs (e.g., quantum dots and polystyrene nanoparticles) based on in vitro cellular uptake data [65], and another recent study showed that there were notable differences between observed and simulated data from a PBPK model that was developed based on in vitro cellular uptake data for gold NPs [51]. IVIVE approaches for NPs have been reviewed [48] and remain to be further studied.
Interspecies extrapolation	It is well accepted that PBPK models are a scientifically-sound tool to perform interspecies extrapolation for small molecules	Only a few studies have attempted to extrapolate PBPK models for NPs from animals to humans using the same approaches used for small molecules [57, 62]. However, the validity of the derived human model has not been extensively evaluated. One study showed that animal-to-human extrapolation of PBPK models for NPs may need to consider biocorona kinetics because there is a longer circulation time in humans than in small rodents [105]
PBPK modeling guidelines	There are multiple guideline documents on how to develop, evaluate/validate, apply, and document PBPK models, such as from the EPA, WHO, and OECD	PBPK modeling guidelines that are specific to NPs are still not available. In fact, a recent study showed that some commonly used PBPK modeling approaches for small molecules, such as route-to-route extrapolation, may not be applicable to NPs [52]
Regulatory acceptance	Multiple regulatory agencies (e.g., EPA, Health Canada, OECD, WHO) accept PBPK models in different areas, such as drug discovery and development and human health risk assessment of environmental chemicals	The PBPK approach by itself is accepted by regulatory agencies in risk assessment of both small molecular chemicals and NPs. Several studies have shown that it is feasible to use PBPK models to assess the human health risk of a few types of NPs, such as silver nanoparticles [106], titanium dioxide nanoparticles [95], and gold nanoparticles [53]. However, formal use of a well-validated PBPK model to assess human health risk of a NP has not been reported by regulatory agencies.

This table is modified based on Table 5 from Lin et al. [46] Table 7 from Lin et al. [107] and Table 1 from Riviere et al. [108]

IVIVE in vitro to in vivo extrapolation, NPs nanoparticles, RES reticuloendothelial system

4.1 General PBPK Principles for Small Molecules and Applicability to Nanomedicines

For small molecules, intravenous injection can be described as a single bolus dose that is directly added to the venous blood compartment. Following extravascular administration, the absorption process can be described as a simple first-order linear absorption process or a more complex mechanistic model, such as the advanced compartmental absorption and transit model for oral absorption [50]. Tissue distribution can be simulated as either a perfusion-limited or a diffusion-limited model structure depending on the physicochemical properties of the chemical (e.g., molecular weight, lipophilicity, and hydrophilicity). Usually, a chemical with a smaller molecular weight and higher lipophilicity is better described using a perfusion-limited model, whereas a chemical with a larger molecular weight and higher hydrophilicity is suitable for a diffusion-limited model. Metabolism of a chemical is usually simulated using Michaelis-Menten equation and the metabolic rate parameters (i.e., V_max and K_m) can be measured using various in vitro systems (e.g., hepatocytes, liver microsomes, and recombinant cytochrome P450) and then extrapolated to in vivo metabolic rates using physiological scaling factors. If experimentally measured data are not available, metabolism can also be simulated using a simple first-order equation, provided that the administration doses of the chemical are within the linear pharmacokinetic dose range. Excretion of chemicals can be through urinary, fecal, and biliary excretion routes, and these excretion processes can be described with either a first-order linear process or a saturable process, depending on the ADME properties and mechanisms of the chemical.

PBPK models can be developed using many different software platforms, including module-based software (e.g., Simcyp, GastroPlus, and PK-Sim), general programming software (e.g., R, Berkeley Madonna, and Python), traditional PK modeling software (e.g., Phoenix), and others (e.g., Excel). Depending on the software program, PBPK modelers may write all the mathematical equations for a new PBPK model if they choose the general programming software. Alternatively, PBPK researchers may use a module-based software platform; in which case, they can choose a prebuilt template and do not need to write the mathematical equations or do any programming.

PBPK models for small molecules are very useful for many different applications mentioned above because these models can be used to predict the target organ dosimetry of chemicals, evaluate drug–drug interactions, perform in vitro to in vivo extrapolation, interspecies extrapolation (e.g., from animals to humans), extrapolation from the healthy to diseased subjects and across life stages, as well as extrapolation across exposure paradigms (e.g., from higher doses to lower doses, from short-term exposure to long-term exposure, and exposure from one administration route to another). However, due to the differences in ADME properties between small molecules and nanoparticles, many of these PBPK modeling strategies that work well for small molecules are not applicable to nanoparticles. For example, studies have shown that traditional route-to-route extrapolation and IVIVE for small molecules are not applicable to nanoparticles [51, 52]. Therefore, many challenges remain in the PBPK modeling of nanoparticles, such as IVIVE and route-to-route extrapolation, as further described below.

4.2 Existing PBPK Models for Nanoparticles

While there are still several challenges for PBPK modeling of nanoparticles, many PBPK models have been developed for different types of nanoparticles. There are already several review articles summarizing the progress and challenges of PBPK modeling for different types of nanoparticles [48, 49, 53‐55]. Gold nanoparticles are most commonly studied or modeled nanoparticle formulations in existing PBPK modeling studies for nanoparticles. There are already multiple published PBPK models for gold nanoparticles [51, 52, 56‐58]. Thus, the methodology for PBPK modeling of gold nanoparticles is relatively well-explored compared with other types of nanoparticles. Understanding the PBPK modeling strategies for gold nanoparticles will provide a foundation to help guide the design of a potential PBPK model for iron–carbohydrate nanoparticles.

Compared with other types of nanoparticles, such as iron–carbohydrate nanoparticles, it is relatively simple to develop PBPK models for gold nanoparticles for the following reasons. First, gold is very stable and does not metabolize, biotransform, or degrade in the body; thus, it is not necessary to consider complex metabolism, dissolution, or biotransformation processes. Second, compared with other metal-containing nanoparticles such as iron oxide, titanium dioxide, and quantum dots, gold nanoparticles are considered inert and relatively safe; thus, it is not necessary to consider any toxicological responses that gold nanoparticles may induce that may change their ADME properties. Additionally, there are reliable and highly sensitive analytical methods, such as inductively coupled plasma mass spectrometry (ICP-MS), that can accurately quantify the plasma and tissue concentrations of gold, thereby providing high-quality PK data to build good-quality PBPK models. All of these factors make gold nanoparticles an ideal example to explore PBPK modeling methodology for nanoparticles in general.

Among published PBPK models, Lin et al. published the first PBPK model for gold nanoparticles in healthy mice after intravenous injection [59]. This PBPK model was developed for different sizes of polyethylene glycol (PEG)-coated gold nanoparticles ranging from 13 to 100 nm. Since the PBPK model structure for gold nanoparticles had not been well established in 2015, the authors systematically evaluated 14 different model structures for different sizes of gold nanoparticles (a relatively small size of 13 nm and a relatively larger size of 100 nm). Based on various model performance statistical metrics, the authors concluded that the most suitable model structure for gold nanoparticles was a membrane-limited model with the consideration of endocytosis of nanoparticles in major MPS organs, such as the liver, spleen, kidney, and lungs. The authors also tried different equations, such as the first-order linear equation, second-order equation, Michaelis–Menten equation, and Hill function to describe endocytosis of nanoparticles. They found that a modified Hill function could best simulate the active cellular uptake process of gold nanoparticles in major MPS organs. By using their optimal model structure and the modified Hill function, the developed PBPK model was able to adequately simulate observed kinetic profiles of different sizes of gold nanoparticles in healthy mice after intravenous injection. Their model structure and the modified Hill function are now commonly applied to develop PBPK models for other types of nanoparticles [49, 60, 61].

Built upon the PBPK model in healthy mice, Lin et al. extrapolated the model to healthy rats and pigs, then conducted an animal-to-human extrapolation by extrapolating the model from each animal species to humans separately, and then compared the performances of the derived three human models by evaluating with a clinical trial dataset of gold nanoparticles in mice [62]. The authors found that the human model derived from the rat model had the most accurate model prediction results, followed by the model derived from the pig model. However, the human model derived from the mouse model had a suboptimal predictive performance. Their results suggest that rats and pigs may be more suitable models than mice in the animal-to-human extrapolation of PBPK modeling of gold nanoparticles. The authors discussed that this finding might be due to several reasons, including different surface coatings, sizes, doses, ages, and/or species/strain/breed among the different studies used in model calibration and evaluation as well as differences in the relative density of phagocytic cells in major MPS organs in different animal species and humans. Overall, this study suggests that animal-to-human extrapolation of the pharmacokinetics of nanoparticles is challenging but possible.

Cheng et al. extrapolated the Lin et al. model from healthy mice to tumor-bearing mice by including a tumor compartment [59, 63]. To rigorously train their model, the authors collected 376 time–concentration datasets in tumors from 200 studies for different types of nanoparticles, including gold nanoparticles and iron oxide nanoparticles. The authors named these 376 tumor datasets as the “Nano-Tumor Database”. By using particle-specific parameters, their model successfully simulated the majority of the collected pharmacokinetic profiles in tumors (i.e., 313 out of 376 datasets). This study suggests that their basic PBPK model structure is applicable to different types of nanoparticles, including superparamagnetic iron oxide nanoparticles and possibly iron–carbohydrate nanoparticles, which will be discussed further.

Based upon the PBPK model structure from Cheng et al. and the Nano-Tumor Database, Chou et al. incorporated machine learning and artificial intelligence approaches into this model to create a so-called artificial intelligence (AI)-assisted PBPK model for different types of nanoparticles [63, 64]. Briefly, by leveraging the data in the Nano-Tumor Database, Chou et al. first developed a quantitative structure–activity relationship (QSAR) model to predict tumor-related critical kinetic parameters (e.g., maximum cellular uptake rate and release rate constants) based on nanoparticles’ physicochemical properties, such as the shape, zeta potential, and hydrodynamic size. To train the QSAR model, the authors evaluated multiple machine learning and deep learning algorithms, such as linear regression, random forest, support vector machine, extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), and deep neural networks. The authors found that the deep neural networks model had the most accurate predictions of the PBPK parameter values. These QSAR model-predicted tumor compartment-related parameters were then incorporated into the PBPK framework to generate the final machine learning-driven or AI-assisted PBPK model for nanoparticles in tumor-bearing mice following intravenous injection.

It should be noted that the above-mentioned PBPK models for gold nanoparticles are all based on single intravenous injection data. Chou et al. extrapolated the model from a single IV route to a multiroute model including intravenous injection, oral gavage, inhalational exposure, and intratracheal instillation [52]. The route-to-route extrapolation was evaluated with extensive time-concentration datasets in plasma and multiple tissues (e.g., liver, kidney, spleen, and lungs) in rats after all these different routes of exposure for different sizes of gold nanoparticles (1.4–200 nm) that were measured using the same analytical method from the same laboratory. The authors found that the traditional route-to-route extrapolation approach that is typically used for small molecules does not work for nanoparticles. By directly extrapolating the model from intravenous injection to other routes of exposure, the resulting model either overpredicted or underpredicted the measured data in plasma or tissues severalfold. The authors found that a multiroute PBPK model for nanoparticles must be calibrated or trained with route-specific pharmacokinetic datasets. The authors explained that, for nanoparticles, upon administration through different routes, the nanoparticles will be in contact with different body fluids, covered by different types of proteins and other biomolecules, forming different biomolecular coronas, which will then determine the biological identity and fate of the nanoparticles in the body. In addition, differences in inflammatory responses following different routes of exposure may change the pharmacokinetic profiles of the nanoparticle. As a result, following different routes of exposure, nanoparticles will form different nanoparticle–protein coronas and exhibit different pharmacokinetic characteristics. Therefore, the traditional route-to-route extrapolation approach for small molecules does not work for nanoparticles.

In vitro to in vivo extrapolation (IVIVE) or correlation (IVIVC) has also been explored for gold nanoparticles. Dubaj et al. (2022) determined the in vitro cellular uptake and in vivo biodistribution of PEG-coated gold nanoparticles and used in silico PBPK modeling to evaluate the IVIVC. The authors measured the cellular uptake and release of PEG-coated gold nanoparticles in different human cell lines, including TH1, A549, HepG2, and 16HBE [51]. The internalization and exclusion kinetics of PEG-coated gold nanoparticles in vitro were modeled using a first-order equation. The authors incorporated the in vitro-derived cellular uptake and release parameters into a PBPK model and compared the model simulations with in vivo experimental data in rats. The authors found there were large differences between experimental and model-predicted concentrations in multiple tissues. The reasons for these discrepancies could be multifaceted, but the authors discussed that the main reason may be the absence of natural barriers in the in vitro conditions. The authors conclude that caution should be taken when extrapolating in vitro cellular uptake data to predict in vivo pharmacokinetics of nanoparticles. However, IVIVE was, to some extent, successfully implemented for other types of nanoparticles [40, 65]. Together, these studies suggest that IVIVE for nanoparticles is complex and may depend on the type of nanoparticles, the adequacy of the in vitro data, and the selection of the cell types. Therefore, the IVIVE approach for nanoparticles remains to be established.

The PBPK modeling strategies based on gold nanoparticles described above have not been applied to develop PBPK models for iron–carbohydrate nanomedicines but have been successfully applied to develop PBPK models for metal oxide-based nanoparticles, such as superparamagnetic iron oxide nanoparticles (SPIONs) [40]. In this study, an in vivo experiment was conducted on mice to characterize tissue biodistribution using magnetization measurements derived from a calibration curve and the superparamagnetic properties of the system, which the authors stated was able to measure up to 1 µg of SPIONs. Final organ concentrations are reported as µg SPION/g tissue. The final PBPK model showed accuracy in predicting SPION behavior in mice, especially in macrophage-rich tissues. The human PBPK model described similar distribution profiles to the murine model. Application of this model to iron–carbohydrate nanoparticles may be tempting. However, there are several caveats to consider. First, while the authors acknowledge that the physicochemical properties of SPIONs can influence the interactions of nanoparticles with plasma proteins potentially altering tissue uptake profiles, this facet was not explored. Many SPIONS are developed to be nanocarriers and to not release iron in the biological tissue, thus exhibiting a fundamentally different structure–function relationship compared with the iron–carbohydrate nanoparticles. Secondly, although the authors generated consistent uptake profiles in murine and human macrophages, quantitation of the SPIONs was achieved using the ferrozine method, which does not distinguish iron derived from SPIONs versus endogenous iron. Although there was an apparent dose–response relationship in the in vivo tissue distribution experiments, the profile of primary iron deposition in liver and spleen changed from the lowest dose (510 mg, spleen > liver) versus the highest administered dose (2040 mg, liver > spleen). This could be attributed to a zero-order PK profile, which has been shown for the iron–carbohydrate complexes but regardless can affect how iron is mobilized or made available for export via ferroportin to serum transferrin [30, 66]. In contrast to the dose dependent macrophage uptake profiles employed in the SPION PBPK model, studies of macrophage uptake of iron–carbohydrate complexes have been challenging to reproduce. Vastly different profiles of the rate and extent of iron uptake are observed between different iron–carbohydrate complexes, suggesting that in vitro tests may not be adequate or experimental conditions need to be optimized to generate parameters for tissue uptake for PBPK models [36]. Another study that evaluated FCM and three analogs with carbohydrate ligand modifications showed statistically significant differences in liver, spleen, and kidney uptake in a chicken embryo model [67]. An additional consideration in application of a SPION PBPK model to an iron–carbohydrate complex PBPK model is effect or parameterization of underlying disease, particularly those that involve inflammation. It is well established that many diseases that require treatment for iron deficiency and iron deficiency anemia (e.g., chronic kidney disease and heart failure) are also associated with systemic inflammation which upregulates hepcidin production, which markedly affects iron efflux from the MPS system [12]. Because of the influence of hepcidin on the pharmacodynamic response, comorbidities should be considered in any PBPK model.

However, a recent study developed a PBPK model for intravenous administration of iron solutions in mice, and then the model was extrapolated to simulate the whole-body distribution of FCM nanoparticles in rats after intravenous administration [68]. This model contained 13 compartments, including plasma, brain, bone, fat, gut, heart, kidney, liver, lung, muscle, skin, spleen, and the rest of the body. These tissues were modeled as individual compartments, because iron distribution data from these tissues were available in mice [69]. The model was initially developed for iron solutions, not for nanoparticles. As such, some mechanisms related to nanoparticle formulations, such as the uptake of nanoparticles by macrophages in MPS organs, were not considered. In addition, the mouse model was built on the basis of data from a single study. The molecular mechanisms that govern the PK of iron were simplified in this model. For example, iron uptake into tissues mediated by transferrin was not considered in this model. The interaction of iron with ferritin was also not considered.

While the PBPK model by Fan et al. (2024) was for iron solutions in mice, the authors extrapolated it to simulate tissue distribution of FCM nanoparticles in rats and humans [68]. During the interspecies extrapolation, all physiological parameters were changed to rat-specific or human-specific. To account for the differences between iron solutions and iron carbohydrate nanoparticles, the authors initially modified the model slightly to consider the direct and indirect release pathways of iron from iron carbohydrate nanoparticles. Regarding the direct release pathway from iron carbohydrate nanoparticles to iron in plasma, since this is a minor pathway (approximately 0.1%) of the total iron dose, this pathway ultimately was not considered to simplify the final model. Regarding the indirect release pathway mediated by the uptake of macrophages, since it mainly occurs at the spleen, the uptake of iron carbohydrate nanoparticles was incorporated into the PBPK model as the spleen blood flow rate. These assumptions and approaches greatly reduced the complexities of the final model. The final rat and human models were able to adequately simulate the selected pharmacokinetic data of iron carbohydrate nanoparticles in rats and humans [11, 70].

The PBPK model by Fan et al. suggests that it is possible to build a PBPK model to simulate plasma pharmacokinetics and tissue distribution of iron solutions and iron carbohydrate nanoparticles in animals and humans, and their model provides a good starting point [68]. However, as acknowledged in their paper, their relatively simplistic model has several limitations. By considering the limitations of the Fan et al. model and to build a mechanistic PBPK model that can inform the design and therapeutics of iron carbohydrate nanoparticles, a new PBPK model structure is proposed as depicted in Fig. 3. Ideally, the following aspects should be considered for a PBPK model for iron carbohydrate nanoparticles. First, the differential uptake mechanisms and storage of iron carbohydrate nanoparticles to different MPS organs should also be considered in the PBPK model. The release of iron from the nanoparticle, the interaction of iron with transferrin, and the transport of transferrin-bound iron to the bone marrow for red blood cell (RBC) production or the liver or spleen for storage should be considered. The recycling pathway when macrophages take up senescent RBCs and release endogenous iron back to the plasma pool should be considered. Note that parameters that are needed to describe these pathways, such as the maximum uptake rate of iron–carbohydrate nanoparticles into macrophages and the release rate of iron from macrophages, are not available for most iron carbohydrate nanoparticles, and different iron–carbohydrate nanoparticles are likely to have different values of these parameters depending on the physicochemical properties of the nanoparticles. These parameters could be measured using validated in vitro cell-based assays (e.g. lysosome tracking and or intracellular ferritin expression) and then incorporated into a PBPK model [40].

Fig. 3

Schematic of a proposed PBPK model structure for iron carbohydrate nanoparticles. A PBPK model for gold nanoparticles. B PBPK model for iron carbohydrate nanoparticles. Each compartment, except plasma, is subdivided into three main components: capillary blood, tissue interstitium, and endocytic/phagocytic cells (PCs). Panel A was adapted from Chou et al. (2022) under the terms of the Creative Commons Attribution 4.0 International License. IH inhalational exposure, IT intratracheal instillation, IV intravenous, RBCs red blood cells.

Bild vergrößern

Another challenge is that different patients will have different levels of endogenous iron, differential local levels of inflammation that may require increased iron loads, thus changing the distribution profiles of iron–carbohydrate nanoparticles, and different pharmacodynamic markers, such as hemoglobin and serum ferritin, which will be quite different among different patient groups, such as healthy anemic patients, diseased anemic patients, and patients with iron deficiency without anemia. These patient-specific physiological factors are inextricably linked to the pharmacodynamic profile and must be considered when building a PBPK model for iron carbohydrate nanoparticles in humans. Finally, one critical aspect of building a validated PBPK model is to evaluate the model prediction with an independent dataset for the same drug formulation or a bioequivalent formulation from a different study. The model by Fan et al. was built on the basis of data from a single study in mice, without independent validation with another mouse dataset, which is a limitation [68]. This limitation should be considered when developing new PBPK models for iron carbohydrate nanoparticles in the future. To obviate the limitations outlined, there are several areas of research that would augment existing data and facilitate parameterization for key aspects of the model. This includes but is not limited to the following data: (1) mechanistic data that describes rates and extents of nanoparticle uptake and intracellular iron trafficking [28, 36], (2) exploratory models that evaluate the viability of species to species extrapolation [11], and (3) conduct of contemporary in vivo pharmacokinetic studies explicitly measuring nanoparticle-bound iron and other relevant iron species (serum iron, transferrin bound iron, and non-transferrin-bound iron species) [8].

5 Summary

Iron deficiency and iron deficiency anemia are disease states that have benefited from nanotechnology for over seven decades, allowing the safe and effective administration of iron parenterally. Despite widespread clinical use, knowledge gaps remain regarding the PK profile of the intact nanoparticles and the complexity of studying PK in vivo due to background endogenous iron homeostasis. Although literature contains a plethora of PK studies on iron–carbohydrate complexes, the PK profiles are generated largely from total serum iron, which contains multiple, dynamic iron species, including drug-bound iron. Additionally, most of the sampling schemes precede uptake into the MPS, hampering dissection of the structure–function relationship. To accelerate the understanding of the PK/PD profiles of this class of complex drugs requires identifying the critical quality attributes for individual iron–carbohydrate complexes and establishing reproducible physicochemical characterization techniques. Only then can translational studies inform parameterization from potential in vitro release tests or cell uptake models for computational models. PBPK models that fully consider the multiple, complex parameters related to iron–carbohydrate nanoparticle use in patient populations have the potential to improve evaluation and clinical use of these complex drugs.

Acknowledgments

The authors acknowledge Dr. Chi-Yun Chen from the Department of Environmental and Global Health, College of Public Health and Health Professions, University of Florida, for helping create the proposed PBPK model structure in Fig. 3.

Declarations

Funding

This work summarizes workshop proceedings from “PBPK Workshop on Iron–carbohydrate Nanomedicines” held 23 and 24 April 2024 at the University of Florida College of Pharmacy, Orlando, FL. Z.L., S.S., and H.G. received honoraria for workshop participation from Vifor (international) AG.

Conflicts of Interest

A.A., B.F., and R.D. are employees of CSL Vifor. V.A., H.G., Z.L., and S.S. report no conflicts of interest.

Availability of Data and Material

Not applicable

Ethics Approval

Not applicable

Code Availability

Not applicable

Author Contributions

All authors made significant contributions to the concept and design of this manuscript, critical review of draft versions of the manuscript, and the provided final approval of the version to be published.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, which permits any non-commercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc/4.0/.

Metadaten
Literatur

Titel: Challenging Traditional ADME Assumptions for Physiologically Based Pharmacokinetic Models for Intravenous Administration of Iron–Carbohydrate Nanomedicines: Potential Utility of Gold Nanoparticle Models as a Roadmap
Verfasst von: Amy Barton Alston
Zhoumeng Lin
Heather Herd Gustafson
Beat Flühmann
Reinaldo Digigow
Vanesa Ayala-Nunez
Stephan Schmidt
Publikationsdatum: 15.08.2025
Verlag: Springer International Publishing
Erschienen in: Clinical Pharmacokinetics / Ausgabe 10/2025
Print ISSN: 0312-5963
Elektronische ISSN: 1179-1926
DOI: https://doi.org/10.1007/s40262-025-01561-w

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Erweiterte Suche

Suchoperatoren:

Springer Medizin

Challenging Traditional ADME Assumptions for Physiologically Based Pharmacokinetic Models for Intravenous Administration of Iron–Carbohydrate Nanomedicines: Potential Utility of Gold Nanoparticle Models as a Roadmap

Abstract

1 Introduction

2 Physical Structure of Iron–Carbohydrate Nanoparticles

3 Absorption, Distribution, Metabolism, and Excretion (ADME) Considerations for Iron–Carbohydrate Complexes in the Context of PBPK Models

3.1 Absorption

3.2 Distribution

3.3 Metabolism

3.4 Excretion

4 Development of PBPK Models for Iron–Carbohydrate Nanoparticles: Challenges and Opportunities

4.1 General PBPK Principles for Small Molecules and Applicability to Nanomedicines

4.2 Existing PBPK Models for Nanoparticles

5 Summary

Acknowledgments

Declarations

Funding

Conflicts of Interest

Availability of Data and Material

Ethics Approval

Code Availability

Author Contributions

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Springer Medizin

Abstract

1 Introduction

2 Physical Structure of Iron–Carbohydrate Nanoparticles

3 Absorption, Distribution, Metabolism, and Excretion (ADME) Considerations for Iron–Carbohydrate Complexes in the Context of PBPK Models

3.1 Absorption

3.2 Distribution

3.3 Metabolism

3.4 Excretion

4 Development of PBPK Models for Iron–Carbohydrate Nanoparticles: Challenges and Opportunities

4.1 General PBPK Principles for Small Molecules and Applicability to Nanomedicines

4.2 Existing PBPK Models for Nanoparticles

5 Summary

Acknowledgments

Declarations

Funding

Conflicts of Interest

Availability of Data and Material

Ethics Approval

Consent to Participate

Consent for Publication

Code Availability

Author Contributions

Drug–Drug Interactions Between Direct Oral Anticoagulants and Other Medications in Patients with Pulmonary Embolism: Results from the Lungenembolie Augsburg (LEA)

Role of Antidrug Antibodies in Oncolytic Viral Therapy: A Dynamic Modelling Approach in Cancer Patients Treated with V937 Alone or in Combination

The Influence of Patient Factors on the Population Pharmacokinetics of Colchicine: Implications for Safe and Effective Dosing

TDM-Based Tailored Dosing of Durvalumab in Lung Cancer Patients: A Comprehensive Population Pharmacokinetic–Pharmacoeconomic Evaluation

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