A Whole-Body Physiologically Based Pharmacokinetic Model for Alpha Particle Emitting Bismuth in Rats

Abstract

Background:

α particle emitting bismuth (²¹²Bi) as decay product of ²¹²Pb-labeled pharmaceuticals has been effective in targeted α particle therapy (TAT). Estimating the contribution of ²¹²Bi released from its chelator to the absorbed doses in nontarget tissues is challenging in TAT. Physiologically based pharmacokinetic (PBPK) modeling can help overcome this limitation. Therefore, a whole-body ²¹²Bi–PBPK model was developed to describe the pharmacokinetics (PKs) of ²¹²Bi in rats.

Materials and Methods:

The rat ²¹²Bi–PBPK model was implemented using the modeling software SAAM II with data and parameter values from the literature. Besides other mechanisms, ²¹²Bi interactions with red blood cells, high molecular weight plasma protein, and intracellular biological thiols are described. Important PK parameters were fitted to time–activity data. Absorbed dose coefficients (ADCs) were calculated for injecting 0.774 fmol of ²¹²Bi.

Results:

²¹²Bi uptake rates of liver, bone, small intestine, bone marrow, skin, and muscle were (0.86 ± 0.13), (3.85 ± 0.63), (0.27 ± 0.05), (1.44 ± 0.29), (0.04 ± 0.01), and (0.007 ± 0.007) per min with corresponding ADCs of 0.09, 0.03, 0.03, 0.07, 0.01, and 0.003 mGy/kBq, respectively. An ADC of 0.70 mGy/kBq was determined for kidneys.

Conclusions:

Kidneys are the dose-limiting organs in ²¹²Bi-based TAT. The ²¹²Bi–PBPK model is an effective tool to investigate the ²¹²Bi biodistribution in murine models. Integrating the ²¹²Bi–PBPK model into other murine and human PBPK models of α particle generators can help study the efficacy and safety of TAT.

Introduction

In vivo α particle generators of long-lived radioactive parents such as ²¹²Pb have been recently used as in vivo sources of α particles through their α particle emitting daughters.^1
–3 However, this concept is limited by the release of ²¹²Bi from the chelator that is subsequently redistributed within the body. The contribution of free ²¹²Bi to absorbed doses in organs at risk depends on the stability of the ²¹²Bi–chelator complex and the physiological uptake in different tissues.⁴ Investigating the pharmacokinetics (PKs) of the free ²¹²Bi is, therefore, vital to estimate the risk of radiation toxicity for accumulating organs, such as kidneys, due to the high biological effectiveness of the emitted α particles.⁵

The systemic biokinetics of bismuth compounds as therapeutic agents were described in a number of preclinical and clinical studies.^6

–12 However, the reports of the PKs of ²¹²Bi are scarce and limited to concentration–time curves because the 60.6 min half-life (t _1/2) of ²¹²Bi is inconvenient for preparations and dissections.¹³ Therefore, most of the studies were limited to either bismuth compounds or radioisotopes with long half-lives, such as ²⁰⁵Bi (t _1/2 = 14.5 d) and ²⁰⁶Bi (t _1/2 = 6.4 d). Consequently, the investigated time interval does not sufficiently cover the early time period after injection, which is relevant for ²¹²Bi. Mathematical modeling can help to understand the PKs and the localization of ²¹²Bi ions and estimate absorbed doses due to the uptake of ²¹²Bi in normal tissues.^14
–16

In this study, a whole-body physiologically based pharmacokinetic (PBPK) model for ²¹²Bi in rats was developed including all relevant physiological mechanisms with parameter values and biokinetic data from the literature.^13,17 The uptake rates of ²¹²Bi by blood and tissues were estimated and tissue absorbed doses were subsequently calculated.

Materials and Methods

²¹²Bi–PBPK model

The developed whole body PBPK model of ²¹²Bi distribution in rats includes all relevant physiological mechanisms such as the distribution of ²¹²Bi through blood flow, transcapillary transport, cellular uptake, and excretion with parameter values from the literature (Supplementary Appendix A1).^{13,17

–26} ²¹²Bi binding to high molecular weight plasma proteins (HWPPs) and its uptake by red blood cells (RBCs) were also taken into account.^27
–29

The rat ²¹²Bi–PBPK model comprises tissues, namely kidneys, liver, spleen, small intestine (SI) representing gastrointestinal track, bones, pancreas, brain, lung, heart, skin, bone marrow (BM), muscle, fat, and remainder of body. Each tissue is divided into vascular, interstitial, and cellular spaces (Fig. 1).

FIG. 1.

²¹²Bi–PBPK model for rats. The model includes main physiological mechanisms to describe the PKs of ²¹²Bi in rats based on its uptake by tissue cells and its association and dissociation with HWPPs and RBCs. Free ²¹²Bi, HWPP- and RBC-bound ²¹²Bi are distributed in the circulation to vascular spaces of body organs followed by free ²¹²Bi diffusion and uptake by tissue cells. ²¹²Bi binds to intracellular thiol molecules and accumulates intracellularly. The α particle emitter ²¹²Bi in each compartment in the model decays with a half-life of 60.6 min.⁴ BM, SI, and RB are BM, SI, and remainder of body. BM, bone marrow; HWPPs, high molecular weight plasma proteins; PBPK, physiologically based pharmacokinetic; PK, pharmacokinetic; RB, remainder of body; RBCs, red blood cells; SI, small intestine. Color images are available online.

The interactions of free ²¹²Bi with HWPPs and RBCs were described by first-order kinetics. Both, HWPP- and RBC-bound ²¹²Bi are confined to the corresponding subspaces in the vascular space of each organ. Free ²¹²Bi diffuses to the interstitium and is passively transported into cells where it binds with high affinity to intracellular metallothionein (MT) metalloproteins and glutathione (GSH) ligands as reported by Hong et al.³⁰ Cellular uptake of free ²¹²Bi was assumed to follow first-order kinetics using an effective value of the intracellular transfer rate of ²¹²Bi due to its interactions with biological thiols.^27,30 Free ²¹²Bi uptake rates by tissue cells were assumed to be proportional to the amount of MT in normal rats because ²¹²Bi ions have higher affinity to MT than to GSH.³¹ Cellular uptake rates of spleen, lung, and pancreas were assumed to be equal to that of SI cells. The uptake rates of heart, brain, fat, and remainder of body were assumed to be equal to that of muscle cells. This assumption was based on studies showing that muscle, skin, brain, and fat have low concentrations of accumulated bismuth.⁶

HWPP- and RBC-bound ²¹²Bi molecules in the vascular space of kidneys are not filtrated through the renal glomerular filtration barrier (GFB) because of their large molecular weight. In contrast, the small molecular weights of free ²¹²Bi and MT- or GSH-bound ²¹²Bi result in rapid filtration through the glomeruli and reabsorption by proximal tubular cells.⁶ A fraction of filtered free ²¹²Bi and MT- or GSH-bound ²¹²Bi is excreted.

Model evaluation and parameter estimation

The ²¹²Bi–PBPK model for rats was implemented using modeling software SAAM II version 2.3 (The Epsilon Group, USA). The SAAM II software supports systems of ordinary differential equations to design and simulate experiments and analyze biokinetic data.³² The ²¹²Bi–PBPK model was evaluated using nondecay corrected percentage of injected dose per gram (%ID/g) data for ²¹²Bi in different tissues of unanesthetized rats (Supplementary Appendix A2).¹³ The %ID/g of ²¹²Bi in the plasma of the virtual rat, that is, the ²¹²Bi–PBPK model, includes the plasma content of free ²¹²Bi and HWPP-bound ²¹²Bi. The injected amount of ²¹²Bi ions in the virtual rat was 0.774 fmol of 88.8 kBq (2.4 μCi), which is the amount used in the experiment.¹³ Values of PK parameters of the model were estimated by data fitting with the implemented Rosenbrock least-squares algorithm using the highest available threshold of the convergence criterion of 10⁻⁷. A relative data-weighting scheme with a standard deviation (SD) of 10% was assigned for all data. The goodness of fit was evaluated using visual inspection, coefficient of variation (CV), and the off-diagonal values of the parameters of the correlation matrix (−0.8 < CM <0.8 for most elements).³³

Dosimetry

Tissue absorbed dose coefficients (ADCs) due to distributed bound and free ²¹²Bi in the virtual rat were calculated. The radioactive daughters of the branched decay of ²¹²Bi, that is, ²⁰⁸Tl (t _1/2 = 3.1 min) and ²¹²Po (t _1/2 = 0.3 μs), were assumed to decay at the site of production. The average energy emitted per decay of ²¹²Bi was assumed to be equal to 7.8 MeV.¹⁸

Results

The time–activity curves for different tissues, that is, kidneys, liver, bone, SI, BM, skin, muscle, plasma, and RBCs, showed acceptable fit (Supplementary Appendix A3) with R ² ≥ 0.94. The estimated values of the PK parameters with the corresponding SD are given in Table 1. The cellular uptake rates of kidneys, liver, BM, bone, and SI were highest. For skin and muscle, low cellular uptake rates were observed. The calculated ADCs (mGy/kBq) in the tissues are given in Table 2.^26,34,35

Table 1.

Model Parameters Fitted to the Experimental Data

Parameter (unit)	Organ	Estimated value	Literature values
Cellular uptake rate of free ²¹²Bi (min⁻¹)	Liver	0.86 ± 0.13	—
	Bone	3.85 ± 0.63	—
	Small intestine	0.27 ± 0.05	—
	Bone marrow	1.44 ± 0.29	—
	Skin	0.04 ± 0.01	—
	Muscle	0.007 ± 0.007	—
First-order association rate (min⁻¹)	RBC conjugated ²¹²Bi	0.010 ± 0.002	0.003 (30)
First-order association rate (min⁻¹)	HWPP conjugated ²¹²Bi	0.20 ± 0.04	—
First-order dissociation rate (min⁻¹)	RBC conjugated ²¹²Bi	0.017 ± 0.007	—
First-order dissociation rate (min⁻¹)	HWPP conjugated ²¹²Bi	0.11 ± 0.03	—
Permeability surface area of free ²¹²Bi (mL/[g·min])	Normal tissues	0.22 ± 0.08	0.1 (23)
Glomerular filtration barrier (L/min)	Kidneys	0.0036 ± 0.0004	0.0013 (31)
Urinary excretion fraction (unity)	Kidneys	0.000	—

The CV of the fitted parameters was <50% for all tissues except muscles with CV ∼100%. All elements of the correlation matrix of the fitted parameters were <0.8.

CV, coefficient of variation; HWPP, high molecular weight plasma protein; RBCs, red blood cells.

Table 2.

Absorbed Dose Coefficients Resulting from the Distribution of 0.77 fmol of Free ²¹²Bi Administered into the Plasma Vein Compartment of the Virtual Rat

Tissue	ADC (mGy/kBq)
Kidneys	0.70
Liver	0.09
Small intestine	0.03
Spleen	0.05
Pancreas	0.04
Bone	0.03
Bone marrow	0.07
Lung	0.06
Brain	0.001
Muscle	0.003
Skin	0.01
Heart	0.004
Fat	0.003
Plasma	0.03
Red blood cells	0.01
Remainder of body	0.003

ADC, absorbed dose coefficient.

Discussion and Conclusions

The PKs of the free α particle emitting ²¹²Bi as a decay product of ²¹²Pb in vivo α particle generators are a critical determinant of the efficacy and safety of targeted α particle therapy (TAT). A whole body ²¹²Bi–PBPK model for rats was developed to determine the values of the PK parameters of the distributed ²¹²Bi and the resulting absorbed doses in tissues.

The estimated first-order association rate of bismuth ions with HWPPs (0.20 min⁻¹) was higher than that with RBCs (0.01/min) within a time frame of two half-lives of ²¹²Bi. Sun et al. and Li et al. reported that bismuth ions bind with high affinity to transferrin and albumin in plasma.^36
–38 The ionic form of bismuth results in rapid binding of bismuth to plasma proteins. Because the GFB depends on the molecular size, the HWPP- and RBC-bound ²¹²Bi would be less likely to enter the ultrafiltrate.⁶ In addition, at low bismuth concentrations, Rao and Feldman pointed out that a smaller fraction of bismuth ions is available for the uptake by rat erythrocytes than at high concentrations.²⁸

Despite the variation in the systemic biodistribution of bismuth depending on the form of injection or route of administration, kidneys are considered as the main sequestering organ for bismuth.^{6,11,39
–41} Bismuth ions are absorbed and sequestered by cysteine-rich intracellular ligands and proteins in the proximal epithelium, such as GSH and MT.^30,42,43 Renal uptake rate was fixed to 1/min based on the results of a local sensitivity analysis. Different uptake values of renal epithelial cells of 0.1, 1, and 10/min were fixed to check how they affect other estimated parameters. The estimated values of fitted parameters deviated <2% for the different rates of renal uptake.

The high uptake rates of ²¹²Bi by bone and BM can be linked to the MT role in bone growth and hematopoiesis.^44

–48 The liver uptake rate was high as expected for a detoxifying organ and was followed by the cellular uptake rates for SI, skin, and muscle. SI, spleen, lung, and pancreas were assumed to have the same bismuth uptake rate. This assumption is based on the report of Russ et al. that spleen, SI, and lung show high concentration of bismuth.⁶ Also, the results of Onosaka and Cherian were considered that SI has the same ability as pancreas to induce and store MT when exposed to Zn salts.³¹ However, the uptakes of these tissues were proposed to be lower than that of the liver as the latter is a detoxifying organ. As gonads are reported to show low concentration of bismuth, the reproductive organs, that is, testes, are expected to have an uptake rate similar to that of muscle. The high estimated CV of the muscle uptake rate is due to the assumption that ²¹²Bi uptake rates of most body tissues, that is, heart, brain, fat, and remainder of body, are equal to that of muscle. The order of the estimated uptake rates is consistent with the reported rank of bismuth concentrations in the tissues of rats.^6,8,40

Tissue sequestering of ²¹²Bi may be related to the abundance of the intracellular MT and GSH relative to bismuth ions, the ability of ²¹²Bi to induce the de novo synthesis of these biological thiols, and the short observation period of the simulation (150 min). The simulated retention of bismuth in tissue cells is compatible with the documented prolonged cell retention of free ²¹²Bi.⁴⁹

Kidneys have the highest ADC (6.5 mGy/kBq) among other tissues. This is in line with the studies that showed that kidneys are the major dose limiting organs in TAT.^50,51 However, the estimated ADC values in normal tissues (Table 2) are expected to be larger than the cases in ²¹²Bi-based TAT. All of the intravenously administered free ²¹²Bi in the tumor-free rat will result in nontarget radiation toxicity. In contrast, in TAT, bismuth will be most probably released from bound or internalized pharmaceuticals at different locations within the body. Therefore, the estimated ADC values may demonstrate the worst-case scenario when all produced ²¹²Bi are dissociated from the targeting pharmaceuticals in the circulation.

The estimated PK parameters of ²¹²Bi can also describe the PKs of the α particle emitter ²¹³Bi. The latter is a decay product of the in vivo α particle generator ²²⁵Ac with an even shorter half-life of 45.6 min. As PBPK modeling allows for the separation between radiopharmaceutical-specific and physiological parameters, it holds promise to integrate the estimated PK parameters of bismuth ions into other PBPK models for mice and humans. As a consequence, the ²¹²Bi–PBPK model may be integrated into other human PBPK models of in vivo α particle generators, such as ²¹²Pb- or ²²⁵Ac-labeled pharmaceuticals, to investigate the fate of free ^212/213Bi radioisotopes as the main challenge encountered in TAT. The β⁻ decay of the bound ²¹²Pb produces different fractions of free ²¹²Bi depending on the chelating systems used. Mirzadeh et al. reported that the ²¹²Pb decay in the ²¹²Pb–1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA) complex results in 36% dissociated ²¹²Bi atoms due to the electronic excitation of the produced ²¹²Bi daughter atoms.⁵² The energy of the emitted gamma after 88% of the β⁻ decays of the parent is transferred to the inner orbital electrons in ∼36% of the decays. The reorganization of valence electrons, induced by the cascade of conversion electrons, emits characteristic X-rays and Auger electrons. Subsequently, these electronic excitations generate a highly ionized Bi⁵⁺ cation, which dissociates from its DOTA chelator.⁵² Using 1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane chelators in ²¹²Pb in vivo α particle generators results in the dissociation of ∼16% of the produced ²¹²Bi from the chelating system.⁴ Also, the model enables for estimating the absorbed doses associated with nonspecific uptake of the distributed free ²¹²Bi in TAT. In consequence, mathematical modeling can be an effective tool to estimate the radiation toxicity associated with the distributed free α particle emitters and assess the efficacy and safety of using in vivo α particle generators in TAT.

Footnotes

Authors' Contributions

N.R.R.Z. designed the study, developed, implemented, and tested the model, performed the simulations, and wrote the article. P.K. evaluated the model, wrote, and edited the article. G.W. discussed the model and edited the article. A.J.B. wrote and edited the article. G.G. designed the study, evaluated the implementation of the model and the simulations, wrote, and edited the article. All coauthors have reviewed and approved the article before submission.

Disclosure Statement

No competing financial interests exist.

Funding Information

The authors gratefully acknowledge the funding from the DAAD (German Academic Exchange Service, Research Grants, Doctoral Programs in Germany 2018/19-57381412) and the Research Campus M² OLIE (German Federal Ministry of Education and Research (BMBF) within the Framework “Forschungscampus–public-private partnership for Innovations” funding code 13GW0389B).

Supplementary Material

Supplementary Appendix SA1

Supplementary Appendix SA2

Supplementary Appendix SA3

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Supplementary Material

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A Whole-Body Physiologically Based Pharmacokinetic Model for Alpha Particle Emitting Bismuth in Rats

Abstract

Background:

Materials and Methods:

Results:

Conclusions:

Introduction

Materials and Methods

212Bi–PBPK model

Model evaluation and parameter estimation

Dosimetry

Results

Discussion and Conclusions

Footnotes

Authors' Contributions

Disclosure Statement

Funding Information

Supplementary Material

References

Supplementary Material

²¹²Bi–PBPK model