Radiobiology of radiolabeled antibody therapy as applied to ... - AAPM

AAPM REPORT NO. 40

RADIOLABELED ANTIBODY TUMOR DOSIMETRY

REPORT OF TASK GROUP NO. 2 AAPM NUCLEAR MEDICINE COMMITTEE

Members Barry W. Wessels, Chairman A. Bertrand Brill Donald J. Buchsbaum Laurence P. Clarke Darrell R. Fisher John L. Humm Timothy K. Johnson Jerry L. Klein Kenneth F. Koral Cheuk S. Kwok Virginia Langmuir Peter K. Leichner Daniel J. Macey George Sgouros Jeffry A. Siegel Edward A. Silverstein Mike Stabin Sven-Erik Strand Evelyn E. Watson Lawrence E. Williams Latresla A. Wilson Ellen D. Yorke Pat Zanzonico April 1993 Published for the American Association of Physicists in Medicine by the American Institute of Physics

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©1993 by the American Association of Physicists in Medicine All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording, or otherwise) without the prior written permission of the publisher.

Published by the American Institute of Physics, Inc. 336 East 45th Street, New York, NY 10017-3463 Printed in the United States of America

CONTENTS Journal Editor’s Preface JohnS.Laughlin......................................................................................

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Co-Editors’ Preface David A. Weber and Amin I. Kassis........................................................................................................................................

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Introduction: Radiolabeled antibody tumor dosimetry Donald J. Buchsbaum and Barry W. Wessels.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Selection of radionuclides for radioimmunotherapy Leonard F. Mausner and Suresh C. Srivastava..................................................................................................................

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MIRD formulation Evelyn E. Watson, Michael G. Stabin, and Jeffry A. Siegel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Pharmacokinetic modeling Sven-Erik Strand, Pat Zanzonico, and Timothy K. Johnson.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Tumor dosimetry in radioimmunotherapy: Methods of calculation for beta particles Peter K. Leichnerand Cheuk S. Kwok.................................................................................................................................

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Microdosimetric concepts in radioimmunotherapy J. L. Humm, J. C. Roeske, D. R. Fisher, and G. T. Y. Chen.. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . , . . . . . . . . . . . . . . .

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Multicellular dosimetry for beta-emitting radionuclides: Autoradiography, thermoluminescent dosimetry and three-dimensional dose calculations E. D. Yorke, L. E. Williams, A. J. Demidecki, D. B. Heidorn, P. L. Roberson, and B. W. Wessels.. . . . . . . . . . . . . . .

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Experimental radioimmunotherapy Donald J. Buchsbaum, Virginia K. Langmuir, and Barry W. Wessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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An overview of imaging techniques and physical aspects of treatment planning in radioimmunotherapy Peter K. Leichner, Kenneth F. Koral, Ronald J. Jaszczak, Alan J. Green, George T. Y. Chen, and JohnC.Roeske......................................................................................,

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Radioimmunotherapy dose estimation in patients with B-cell lymphoma J. A. Siegel, D. M. Goldenberg, and C. C. Badger.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Dosimetry of solid tumors Ruby F. Meredith, Timothy K. Johnson, Gene Plott, Daniel J. Macey, Robert L. Vessella, Latresia A. Wilson, Hazel B. Breitz, and Lawrence E. Williams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Dosimetry of intraperitoneally administered radiolabeled antibodies John C. Roeske, George T. Y. Chen, and A. Bertrand Brill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Radiobiology of radiolabeled antibody therapy as applied to tumor dosimetry V. K. Langmuir, J. F. Fowler, S. J. Knox, B. W. Wessels, R. M. Sutherland, and J. Y. C. Wong . . . . . . . . . . . . . . . . .

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Journal Editor’s Preface The AAPM, through its Science Council, asked Medical Physics to accept the responsibility for the scientific review of all of the manuscripts proposed for this report and to consider the final manuscripts for publication in Medical Physics. This responsibility was accepted by the Editor and Editorial Board. The Editor then asked Dr. David A. Weber, Associate Editor and Head of Nuclear Medicine Research at the Brookhaven National Laboratory, and one of his scientific colleagues, Dr. Amin I. Kassis, Director of Radiation Biology, Brigham and Women’s Hospital, Harvard Medical School, to accept the responsibility for scientific reviews of the material to be provided for the report and to serve as the Co-Editors of a special issue of the journal. This arrangement was approved by the Science Council of the AAPM and by the Editorial Board. This review, a major task, has been carried out in a comprehensive and scientifically rigorous manner by the Editors for this special issue with the vital assistance of the expert referees, authors and Task Group members. Medical Physics appreciates the decision of the Task Group to offer this important collection of articles written by authorities in the field of radiolabeled antibody tumor dosimetry for publication in the AAPM journal. John S. Laughlin

Co-Editors’ Preface Monoclonal antibodies have been considered particularly appealing as selective carriers of diagnostic and therapeutic radionuclides in vivo. Their target specificity continues to attract investigators to identify and produce new agents for clinical use. In spite of the limited number of clinical applications at present, it is extremely important that factors influencing the localization and clearance properties of radioimmunoconjugates, especially tumor-associated, antigen-specific antibodies, be considered and understood by those administering them to patients so as to assess those variables that influence the absorbed radiation dose from internal emitters. The absorbed radiation dose has been, and will continue to be, a pivotal factor in assessing the risks and therapeutic utilities of radiopharmaceuticals. The AAPM Nuclear Medicine Task Group, under the leadership of Dr. Barry Wessels, sought qualified experts in various specialties concerned with the dosimetry of radiolabeled antibodies to develop a well-balanced review of the multiple concerns and factors that influence the clinical use of radiolabeled anti-tumor antibodies. Dr. Donald J. Buchsbaum, a member of the Task Group, chaired a subcommittee responsible for coordinating and overseeing the preparation of all manuscripts. In the 13 manuscripts produced, many of the approaches employed to estimate absorbed radiation dose in radioimmunotherapy have been evaluated, and the physical, physiologic, chemical, and biologic parameters affecting tumor dosimetry presented. In addition, the decay properties of various radionuclides and their radiobiologic effects have been discussed, and dose calculations at the organ, tissue, cellular, and subcellular levels compared. The manuscripts, containing extensive, up-to-date reference lists, will be very useful to those interested in the use of radiolabeled antibodies in the diagnosis and treatment of disease. We are pleased to have had the opportunity to explore with the authors the multifaceted topic of radiolabeled-antibody tumor dosimetry. Since many of the experts in this field are contributors to this supplement, it required some extra attention to find equally qualified referees. Having accomplished this, we would like to express our sincere gratitude to those who have volunteered their time to review and comment on the manuscripts. David A. Weber and Amin I. Kassis

Introduction: Radiolabeled antibody tumor dosimetry Donald J. Buchsbauma) Department of Radiation Oncology, University of Alabama at Birmingham, Birmingham, Alabama 35233-6832

Barry W. Wessels Department of Radiology, George Washington University Medical Center, Washington, DC 20037

(Received 18 March 1992; accepted for publication 8 January 1993)

I. INTRODUCTION Through the sponsorship of the Nuclear Medicine Committee of the American Association of Physicists in Medicine (AAPM), a Nuclear Medicine Task Group 2, “Dosimetry of Radiolabeled Antibodies” was established in July 1987 under the Chairmanship of Dr. Barry Wessels to produce reports on radiolabeled antibody dosimetry, which would include an extensive literature search and an analysis of how to approach the dosimetry to normal tissues and tumor of radiolabeled antibody therapy (radioimmunotherapy). The first report published in 1990 1 summarized a “Bone Marrow Dosimetry and Toxicity for Radiolabeled Antibodies” symposium held in conjunction with the 1988 American Society for Therapeutic Radiology and Oncology (ASTRO) annual meeting. In 1989, the Steering Committee on the Nuclear Medicine Task Group 2 decided at the Society of Nuclear Medicine (SNM) Annual Meeting that the new focus area for the Task Group would be tumor dosimetry for radiolabeled antibody therapy. The Task Group members and invited guests active in radiolabeled antibody research from the physics, radiation biology, nuclear medicine, and oncology communities had been invited to attend meetings to plan and prepare this report on “Radiolabeled Antibody Tumor Dosimetry.” These meetings were held in conjunction with the annual meetings of the ASTRO, the AAPM, the SNM, the “International Conference on Monoclonal Antibody Immunoconjugates for Cancer” and the “Third Conference on RaRadioimmunotherapy of and dioimmunodetection Cancer.” The purpose of this report is to provide an extensive literature search and review the various approaches that are being pursued in preclinical and clinical studies to estimate tumor dosimetry associated with radioimmunotherapy (RIT), and to suggest future directions for dosimetry research in this field. Included in this report is a discussion of the radiobiological aspects of tumor dosimetry of radiolabeled antibody therapy. Radiolabeled monoclonal antibodies (MoAbs) offer the potential of highly localized, targeted radiation treatment of cancer. The effectiveness of radiation treatment of malignant disease is correlated with the total dose delivered, with increasing dose producing increasing cell kill. Similarly, normal tissue damage is also directly related to the total dose deposited. The ability to quantify the dose delivered to tumor and normal tissues when using radiolabeled MoAbs has been a perplexing problem. As noted in the review of a National Cancer Institute workshop, 2 techniques for evaluating the dosimetry of ra499

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diolabeled antibody therapy are essential to support the development of RIT in the treatment of neoplastic diseases. Radiation dosimetry is important for treatment planning and the assessment of results. It is necessary to determine the quantity of radiolabeled antibody to administer to maximize the radiation dose to the tumor while not exceeding tolerance levels of critical normal tissues, In contrast to external beam radiation therapy dosimetry, the tumor dosimetry for radiolabeled antibody therapy is dependent on a number of variables including: ( 1) kinetics of biodistribution, tumor uptake and retention of the radiolabeled antibody, (2) the uniformity of distribution of the radiolabeled antibody within tumor, (3) the radionuclide attached to the antibody, and (4) the radiobiological response of tumor cells to continuously decreasing low-doserate radiation. The 12 papers in this special issue of Medical Physics summarize the problems, various techniques that are being used to estimate the tumor dosimetry associated with radiolabeled antibody therapy, and future directions as highlighted below. II. TOPICS DISCUSSED IN THIS REPORT A. Selection of radionuclides for RIT The contribution by Mausner and Srivastava 3 to this special issue reviews the factors that influence the choice of a radionuclide for RIT. A potential advantage of some of the radionuclides would be a higher tumor/whole-body dose, resulting in less toxicity to normal tissue, particularly bone marrow. It is essential to carefully consider the choice of radionuclide in conjunction with the in vivo pharmacokinetic (localization and clearance in tumor and normal tissues) properties of the radiolabeled MoAb, the physical half-life of the radionuclide, the chemistry of conjugation to MoAbs, and the toxicity of free radionuclide. The choice of radionuclide also depends on the microdistribution of the radiolabeled MoAb relative to the radiosensitive target sites, involving uniform versus nonuniform deposition in tumors or localization on cell surfaces versus internalization of radionuclides to the cell cytoplasm or nuclei. To optimize the efficacy of RIT, it will be necessary to develop combinations of MoAbs or antibody fragments and radionuclides whose pharmacokinetics, physical halflives and emissions are matched to give the largest possible tumor dose and the least normal tissue toxicity, i.e., the largest possible therapeutic ratio.

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B. MIRD formulation The approach developed by the Medical Internal Radiation Dose (MIRD) Committee of the Society of Nuclear Medicine for the estimation of average absorbed dose from internally deposited radionuclides has been applied to radiolabeled MoAb therapy in animals and humans, as described in the paper by Watson et al. 4 in this report. The classic MIRD formulation widely used for macroscopic dosimetry problems assumes a uniform distribution of cumulated activities of radiolabeled MoAbs within each source region and a uniform deposition of energy within each target region. The experimental animal and clinical patient studies clearly demonstrate that radiolabeled MoAbs are not uniformly distributed within solid tumors. There are point-source calculations available within the MIRD pamphlets to deal with the problem of dose heterogeneity encountered in RIT. In addition to the problem of nonuniform uptake of radiolabeled MoAbs in solid tumors, the macroscopic MIRD approach does not distinguish between a uniform distribution of radiolabeled MoAb that binds to the cell surface and a uniform distribution of nonspecific radiolabeled MoAb. Conventional MIRD type calculations for radiolabeled MoAbs give approximate average dose estimates which may not be sufficiently accurate, especially for alpha and Auger emitters. With these types of radionuclides, a microdosimetric approach will be required, as described below. C. Pharmacokinetics modeling Pharmacokinetics modeling involves an attempt to estimate the biokinetics of tumor and normal organ uptake of radiolabeled MoAbs on both a macroscopic and microscopic level, and then to perform the dosimetric calculations. It is an essential component for estimation of cumulated activities in the various source regions of the body. Research is still required to find accurate and predictive models of both macroscopic and microscopic pharmacokinetics. This subject is reviewed by Strand et al. 5 D. Calculation techniques for RIT Leichner and Kwok6 in this report provide a critical analysis of the calculational approaches that have been used for beta particle tumor dosimetry in RIT. In modeling of absorbed dose distributions, analytical, numerical, and Monte Carlo methods have been used to investigate the effects of uniform and nonuniform activity distributions associated with RIT. E. Microdosimetry Alpha emitters and internalized Auger electron emitters may be useful in RIT because of their high LET and RBE. However, the methodology to calculate dosimetry for short range alpha emitters and internalized Auger emitters must consider energy deposition at the cellular and subcellular level. Such a microdosimetric approach which analyzes the Medical Physics, Vol. 20, No. 2. Pt. 2, Mar/Apr 1993

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effect of source microdistribution on individual cells has been taken by a number of investigators, because of the limitations of the macroscopic MIRD formulation and the nonuniformity of the radiolabeled antibody in tumor. Humm et al.7 in this report summarize approaches that are being used to estimate the microdosimetry of RIT. It should be noted, however, that microdosimetry estimates are based on modeling and are difficult to substantiate experimentally. F. Autoradiography, thermoluminescent dosimetry, and three-dimensional dose calculations Radionuclide activity variations within tumors can be measured by quantitative autoradiography. However, quantitative autoradiography alone cannot provide total dose measurements, because of the temporal change in radiolabeled antibody uptake, penetration, and clearance.’ Yorke et al.8 note that autoradiography and thermoluminescent dosimetry are complementary techniques. Autoradiography shows the activity distribution at a particular point in time, whereas TLDs are integrating dosimeters performing spatial and temporal integrations within the volume they occupy, and can be used to calibrate the autoradiographs. Griffith et al9 and Roberson et al.10 c o n v e r t e d d a t a from serial autoradiographs to derive three-dimensional activity matrices in animal tumor xenografts. Using point source function calculation techniques, two-dimensional isodose curves’ or three-dimensional dose-rate curves 1 0 were generated showing marked dose heterogeneity in most tumor systems examined. Further studies remain to be performed to be able to relate the dose-rate distributions to time averaged dose distributions, cell kill, and eventually to therapeutic efficacy. G. Experimental RIT Radiolabeled MoAbs have been used for RIT of spheroids and a variety of murine syngeneic tumors and human tumor xenografts. The results are summarized in the paper by Buchsbaum et al. in this report.” The approaches taken to estimate tumor dosimetry in the experimental animal studies include the MIRD approach, thermoluminescent dosimetry, autoradiography, and comparison to external beam irradiation. The uniform geometry of the spheroid has facilitated the estimation of radiation dose. The two most important factors for therapeutic efficacy in the spheroid model are good penetration of the radiolabeled MoAb and an adequate half-life of the radionuclide to exceed the time of penetration. The results in animal studies indicate that MoAbs radiolabeled with a variety of radionuclides have been effective in inhibiting tumor growth or producing cures against a variety of tumor types. The majority of investigators have estimated the dose to tumor using the MIRD formalism. A few investigators have estimated the dose to tumor using TLDs and autoradiography. The effectiveness of RIT depends on a variety of factors including antibody specificity, affinity and immunoreactivity, tumor vascularity, and differential radiation sensitivity

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of the various tumor types. It must be kept in mind that there are limitations of spheroid and animal models in modeling what occurs in the clinical situation. 11,12

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is a potential advantage in therapeutic ratio predicted for alpha particle radiation when bone marrow (high linearquadratic alpha/beta ratio) is considered as the critical organ. 17

H. Imaging techniques and treatment planning Leichner et al. 13 in another section of this report have reviewed the various imaging techniques that have been used for RIT treatment planning. They discuss tumor and normal organ volume computations from CT and MRI data, correlative image analysis, and treatment planning for RIT. I. Clinical studies with dosimetry There have been a large number of clinical RIT studies that have included tumor dosimetry estimates. The approaches that have been taken in lymphoma, solid tumors, and intraperitoneal therapy are described in three manuscripts in this report. 14-16 Radiation dosimetry in B-cell lymphoma patients has been done using the MIRD approach. Organ and tumor radionuclide activity measurements have usually been done with conjugate view planar scintillation camera imaging. 14 Organ and tumor volumes have been obtained by CT, SPECT, or the published values of the MIRD committee. The range of tumor absorbed dose estimates in five clinical lymphoma studies is reported.1 4 For solid tumors, the MIRD approach, planar imaging and tumor volumetrics have been performed in a similar manner as in lymphoma studies. 15 There have been wide variations in estimated tumor doses in different studies, and no definite dose-response relationship has been observed. The spatial resolution limits of planar or SPECT imaging devices prevents detection of the nonuniformity of radiolabeled MoAb deposition, and thus permits only the estimation of average dose to tumor. Regional administration of radiolabeled MoAbs has been used in the peritoneum, the cerebral spinal fluid, the pleural/pericardial cavity, and within cystic brain tumors. Roeske et al.16 have reviewed the methods and results that have been used for intraperitoneal dosimetry. J. Radiobiology of RIT Langmuir et al.17 elsewhere in this report reviewed the information available on the radiobiology of low-dose- rate external beam irradiation and RIT as applied to tumor dosimetry, and have discussed comparisons between the two. Langmuir et al. 17 have concluded that tumors most likely to respond to RIT would be those types that are inherently radiosensitive, those with a poor capacity to repair radiation damage or with long repair half-times, those tumors that are susceptible to blockade in sensitive phases of the cell cycle, and tumors that reoxygenate rapidly. A comparison of alpha and beta emitters for RIT indicates an advantage for beta emitters if the linear-quadratic alpha/beta ratio for tumors is greater than that of the critical organ of toxicity, as is the usual case. However, there

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ACKNOWLEDGMENTS We thank Donell Berry for typing the manuscript. Supported by NIH Grant CA44173 and the Elaine Snyder Cancer Research Award. “Correspondence should be sent to: Donald J. Buchsbaum, Ph.D., Department of Radiation Oncology, University of Alabama at Birmingham, 619 South 19th Street. Birmingham, AL 35233-6832. 1 J. A. Siegel, B. W. Wessels, E. E. Watson, M. G. Stabin. H. M. Vriesendorp, E. W. Bradley, C. C. Badger, A. B. Brill, C. S. Kwok, D. R. Stickney, K. F. Eckerman. D. R. Fisher, D. J. Buchsbaum, and S. E. Order, “Bone marrow dosimetry and toxicity for radioimmunotherapy,” Antib. Immunoconj. Radiopharm. 3, 213-233 (1990). 2 S. A. Leibel, S. E. Order, D. R. Fisher, J. R. Williams, and R. J. Morton, “Physics and biology of radiolabeled antibodies workshop, sponsored by the Radiation Research Branch, National Cancer Institute, Division of Cancer Treatment, February 12-13, 1987, Bethesda, Maryland,” Antib. Immunoconj. Radiopharm. 1, 271-282 (1988). ‘L. F. Mausner and S. C. Srivastava, “Selection of radionuclides for radioimmunotherapy,” Med. Phys. 20, 503-509 (1993). 4 E. E. Watson, M. G. Stabin, and J. A. Siegel, “MIRD formulation,” Med. Phys. 20, 511-514 (1993). 5 S.-E. Strand, P. Zanzonico, and T. K. Johnson, “Pharmacokinetic modeling,” Med. Phys. 20, 515-527 (1993). 6 P. K. Leichner and C. S. Kwok, “Tumor dosimetry in radioimmunotherapy: Methods of calculation for beta particles,” Med. Phys. 20, 529-534 (1993). 7 J. L. Humm, J. C. Roeske, D. R. Fisher, and G. T. Y. Chen, “Microdosimetric concepts in radioimmunotherapy,” Med. Phys. 20, 535-541 (1993). 8 E. D. Yorke, L. E. Williams, A. J. Demidecki, D. B. Heidorn, P. L. Roberson, and B. W. Wessels, “Multicellular dosimetry for betaemitting radionuclides: Autoradiography, thermoluminescent dosimetry and three-dimensional dose calculations,” Med. Phys. 20, 543-550 (1993). 9 M. H. Griffith, E. D. Yorke, B. W. Wessels, G. L. DeNardo, and W. P. Neacy, “Direct dose confirmation of quantitative autoradiography with micro-TLD measurements for radioimmunotherapy,” J. Nucl. Med. 29, 1795-1809 (1988). 10 P. L. Roberson, D. J. Buchsbaum, D. B. Heidom, and R. K. Ten Haken, “Three-dimensional tumor dosimetry for radioimmunotherapy using serial autoradiography,” Int. J. Radiat. Oncol. Biol. Phys. 24, 329-334 (1992). 11 D. J. Buchsbaum, V. K. Langmuir, and B. W. Wessels, “Experimental radioimmunotherapy,” Med. Phys. 20, 551-567 ( 1993). 12 B. W. Wessels, “Current status of animal radioimmunotherapy,” Cancer Res. (Suppl.) 50, 970s-973s (1990). 13 P. K. Leichner, K. F. Koral, R. J. Jaszczak, A. J. Green, G. T. Y. Chen, and J. C. Roeske, “An overview of imaging techniques and physical aspects of treatment planning in radioimmunotherapy,” Med. Phys. 20, 569-577 (1993). 14 J. A. Siegel, D. M. Goldenberg, and C. C. Badger, “Radioimmunotherapy dose estimation in patients with B-cell lymphoma,” Med. Phys. 20, 579-582 (1993). 15 R. F. Meredith, T. K. Johnson, G. Plott, D. J. Macey, R. L. Vessella, L. A. Wilson, H. B. Breitz, and L. E. Williams, “Dosimetry of solid tumors,” Med. Phys. 20, 583-592 (1993). 16 J. C. Roeske, G. T. Y. Chen, M. Reese, and A. B. Brill, “Dosimetry of intraperitoncally administered radiolabeled antibodies,” Med. Phys. 20, 593-600 (1993). 17 V. K. Langmuir, J. F. Fowler, S. J. Knox, B. W. Wessels, R. M. Sutherland, and J. Y. C. Wong, “Radiobiology and radiolabeled antibody therapy as applied to tumor dosimetry,” Med. Phys. 20, 601-610 (1993).

Selection of radionuclides for radioimmunotherapy Leonard F. Mausner and Suresh C. Srivastava Medical Department, Brookhaven National Laboratory, Upton. New York I I973 (Received 18 March 1992; accepted 6 October 1992)

I. INTRODUCTION The potential of utilizing monoclonal antibodies (MoAb) as carriers of radionuclides for the selective destruction of tumors (radioimmunotherapy, RIT) has stimulated much research activity. The approach should be specially beneficial for treatment of tumors not easily amenable to surgical control, for treatment of early recurrence and of distant metastases. However, from dosimetric and other considerations, the choice of radiolabel is an important factor that needs to be optimized for maximum effectiveness of RIT. Most therapeutic trials to date have utilized 131 I, largely due to its ready availability at moderate cost, the ease of halogenation techniques for proteins, and its long history of use in treating thyroid malignancy, rather than any careful analysis of its suitability for RIT. This paper briefly reviews the present and future radionuclides that are considered particularly suitable for RIT. II. SELECTION CRITERIA The selection criteria must be based on the physical data about the radionuclide, its production and chemistry and the biological variables governing its use. The important physical variables to consider include the radionuclide half-life, the type, energy, and branching ratio of particulate radiation and the gamma-ray energies and abundances. It is important to match the physical half-life with the antibody in vivo pharmacokinetics. If the half-life is too short, most decay will have occurred before the MoAb has reached maximum tumor/background ratio. Conversely, considerations of tumor radiobiology and low radionuclide/antibody specific activity may also limit the use of long-lived radionuclides. For equal radioactivity concentrations in the target, radionuclides with long half lives will produce a lower absorbed dose rate than those with short lifetimes. If the maximum absorbed dose rate from beta particles is much lower than that typical in brachytherapy (40-64 cGy/h), cell kill per cGy is decreased.1,2 The theoretical low specific activity of longer lived radionuclides would thus require a large mass of radionuclide, ligand, and antibody to achieve adequate dose rate. This can make the use of long-lived radiolabels less desirable. However, if a two or three-stage therapy approach is utilized,3 it becomes useful to consider the use of long-lived beta emitters, e.g., 3 2P and others. To some extent the problem of low target dose rate may be counteracted by a number of factors including high nonpenetrating equilibrium dose constant, high target to nontarget ratio, high carrier labeling efficiency, and the ability to administer a large protein mass (tumor saturation effect). The type of particulate emission also must be considered. The potent lethality of Auger and low-energy conver503

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sion electrons has been demonstrated. 4-8 This effect can best be realized with intranuclear localization of the radionuclide, which does not generally occur with radiolabeled MoAb. Of course, a particles have a high linear energy transfer (LET) effective in cell killing and a range of several cell diameters, 40-80 µm. The short ranges will accentuate inhomogeneous absorbed dose particularly when the MoAb deposition is inhomogeneous. Beta particles are less densely ionizing and have a range longer than a’s so that the distribution requirements are less restrictive for RIT of bulky disease. On the other hand, for micrometastases, the absorbed fraction for higher energy beta particles (range > tumor size) is decreased, leading to a less favorable tumor absorbed dose. The gamma-ray energies and abundances are also important physical properties, because the presence of gamma rays offers the possibility of external imaging but also adds to the whole body dose. These physical properties alone can be used to calculate radiation absorbed dose at the cellular level. This approach has been used by Jungerman et al. 9 to estimate delivered doses for RIT. An approach which explicitly includes biodistribution and kinetic data by using an idealized time-dependent averaged target-to-nontarget uptake ratio is that of Wessels and Rogus.1 0 Although the quantitative dose ratios are highly dependent on the input biodistribution data, a comparison of the relative effectiveness of the radiolabels was demonstrated. This relative efficacy was approximately constant for reasonable variation of model parameters in accordance with observed biological data. A similar approach was used recently by Yorke et al. 11 Also, Humm1 2 has considered the effect on MoAb dosimetry of varying tumor size and of cold regions. These papers underscore the importance for therapy of a high ratio of nonpenetrating to penetrating (γ) radiations. The complex relationship between tumor curability with different radionuclides and tumor size has been reviewed by Wheldon and O’Donoghue. 13 The main chemical variables to be considered in choosing a radionuclide for therapy with monoclonal antibodies are the radionuclide specific activity achievable, metal-ion contamination, the number of labels per MoAb molecule obtainable without loss of immunological activity, and the stability of the radionuclide-protein attachment. The specific activity, or amount of activity per mass of the element in question (MBq/mg), depends primarily on the method of production. Simple neutron absorption reactions (e.g., n ,γ) generally give low specific activity since the radionuclide cannot be chemically separated from a target of the same element. Accelerator-based proton, deuteron, or alpha-induced reactions are intrinsically no-carrier-added (NCA) methods that do allow chemical separation of

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product from the target. This can also be achieved at reactors by neutron absorption reactions leading to an intermediate product with a beta decay to the desired final product, or by fast neutron reactions such as (n,p). The achievable specific activity of these NCA methods then largely depends on the impurity levels of the product element in the target or in various reagents used in processing. An often overlooked source of carrier is due to the direct production of stable isotopes of the product element. Although this effect is often negligible compared to carrier introduced with the target, it can become significant with very pure targets and high bombarding energies. With increasing energy, the typical peaks in nuclear excitation functions broaden, usually reaching a plateau at approximately 150-200 MeV and reaction cross sections for neighboring isotopes become comparable over large energy ranges. Some of these issues have been reviewed recently for therapeutic radionuclides.1 4 The presence of metal ions other than the product is a concern as they can compete for binding sites on chelateMoAb conjugates. It is largely controlled by the selectivity of the chemical separation scheme, but this process is not perfect. For example, a normally adequate separation factor of 10-7 on a 10 g target still leaves 1 µg of target in the product which may be of concern when labeling at low protein concentrations. Indeed, measurement of these stable species at low concentration in radioactive solutions is often a very difficult practical problem. Although various analytical procedures exist for detecting ions at subpart per million levels, for example atomic absorption, emission spectroscopy, and x-ray fluorescence, these techniques often take time, utilize expensive instrumentation, and may require a large fraction of the final product solution for the measurement. Generally, the sooner the radionuclide is used the better, because its specific activity is highest, and this need competes with the desire to measure the specific activity and the impurity levels. Also, it is typical for many research groups that the expensive analytical apparatus is not wholly owned. Instead, access is through a shared-use facility whose operators are very reluctant to introduce radioactive material into their equipment. Thus the fastest, albeit indirect method, of determining carrier levels may simply be by titration with chelate during labeling. The convenience, efficiency, and gentleness of various radiolabeling procedures as well as the stability of the radionuclide attachment to the antibody are all very important factors which are being actively investigated by many groups. They will not be considered further here as these topics are beyond the scope of this paper and have been reviewed several times.15-18 While recognizing the difficulties in designing new conjugation schemes, at this point, it is simply assumed that adequate radiolabeling techniques either exist or will become available for use with radionuclides to be discussed.18 However, another practical aspect to be considered is that of radionuclide production-the routine availability, at reasonable cost, of quantities of radioactivity suitable for therapy. At present, only 131 I truly meets all of these production criteria. However, this situMedical Physics, Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

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ation is changing for several other attractive radionuclides to be discussed below. These physical and chemical factors must then be viewed in light of available biological information. There is substantial variation in antibody uptake, macro- and micro-distribution, kinetics and processing (metabolism/ catabolism) depending on the particular antibody, antibody dose, the variability of antigenic expression in the tumor, its size and stage, etc. Limitations due to normal tissue radiotoxicity are not entirely the function of radionuclide emissions but are largely governed by the pharmacokinetics of the antibody. For many of the MoAbs and MoAb fragments currently being investigated for immunotherapy some generalities emerge. It is generally believed that one-half to three days is usually required to reach maximum tumor uptake19-22 although optimum contrast with whole MoAbs may take longer. Despite the presence of numerous antigen sites on cancer cells, evidence from tumor implanted microthermoluminescent dosimeter 25 p r o b e s 2 3 , 2 4 and autoradiography indicates a nonuniform cellular distribution of the MoAb in most cases. This may be due to cell type heterogeneity, 26 heterogeneity of antigenic expression,27 poor delivery, and spatial inaccessibility. These factors considerably reduce the attractiveness of short-ranged alpha-emitting radionuclides for radioimmunotherapy. A role for alpha emitters may be feasible in specific cases such as for micrometastases or intracavitary administration for some types of cancers, such as peritoneal injection for ovarian carcinoma. 28,29 The longer range of beta particles can still permit uniform tumor irradiation despite a marked heterogeneity of distribution of radioactivity within the tumor. It appears desirable to deliver ionizing radiation with a range of one to several millimeters in tissue, as from intermediate to high-energy beta particles. Ill. CANDIDATE RADIONUCLIDES Relatively few alpha emitting radionuclides have been considered for RIT. Bismuth-212 (t1/2= 60.5 min, E α = 7.8 MeV) and 2 1 1At ( t1/2 = 7.2 h, E α = 6.8 MeV) are the two nuclides that have been most studied. 30-36 The 212 Bi can be available via a 2 2 4Ra generator system,37 while 2 1 1At is accelerator produced.38,39 The short half-life of 2 1 2 Bi is not well matched to MoAb uptake kinetics but it might be possible to conjugate its parent 212 Pb, with a 10.6 h halflife, to a MoAb or MoAb fragment and thus generate the alpha emitter in vivo. The feasibility of this approach is 212 under investigation.4 0 Nevertheless, the peak of B i growth occurs at 3.8 h which is probably still too short for the peak in tumor uptake. The short life time of 211 At and limited availability may impede its use except in very special situations.4 1 It has been suggested 28 that the 20.1 h half-life of 255 F m is more appropriate for RIT. Unfortunately this nuclide and similar alpha emitting heavy radionuclides (atomic number > 82) are the parents or members of long decay chains involving both alpha and beta emission. Because the nuclear recoil from the alpha (and some of the beta) decays are considerably more energetic than chemical bond strengths, these transitions are capable of rupturing the

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radionuclide-ligand bond. Unless the daughter half-life is less than a few minutes it will be free to diffuse away from the tumor. Worse still, most of these heavy elements tend to irreversibly lodge in bone. Beta emitters offer a much wider choice of candidates with a selection of particle ranges and chemical properties. The use of radionuclides with some gamma emission would allow diagnostic low-dose experiments to determine biodistribution prior to administering a therapeutic dose of the exact same preparation. This is a real advantage because it has been observed 42,43 that the biodistribution can be influenced by the choice of radionuclide alone, even with the same chelate-antibody complex. It is possible that these differences reflect the redistribution of the radioactivity following catabolism of the antibody after localization. Clinically it may be necessary to image each patient prior to therapy in order to assess antigenic status and to calculate tumor and sensitive tissue doses from the observed biodistribution. The disadvantage of this choice is that, because of the penetrating nature of the gamma radiation, a less than optimum target/nontarget dose ratio may result. Preferably, the g energy should be below 300 keV and the g abundance sufficient for visualization in vivo A number of attractive radionuclides and their properties are listed in Table I.44 Of these, 6 7 Cu has been previously identified as possessing attractive physical properties for RIT,10 and is being actively investigated by several groups. 45-47 Another advantage is that 67Cu, upon eventual dissociation from its ligand in vivo, does not preferentially localize in bone, kidney, or liver, in contrast to many other radiometals. Al153 though the pharmaceutical Sm-ethylenediaminetetramethylenephosphonic acid (EDTMP) shows potential as a bone cancer agent,48,49 very little has been reported on the use of 1 5 3 Sm as an antibody label. 50 However, as can be seen from Table I its physical properties fulfill many criteria discussed above. Similarly, 1 0 5Rh has received some attention,” and more recently 4 7S C (Refs. 52,53) and Medical Physics, Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

Au.54,55 Iodine-131 is in the therapeutic class but clearly its long half-life and high abundance of 364 keV photons make for less attractive tumor/nontarget dose ratios than the other candidates. Nevertheless, due to its ready availability, ease of labeling, and more rapid clearance from kidney and liver than most metal chelates particularly when using methods that produce negligible dehalogenation in vivo,56-59 it has been widely used for RIT (e.g., Refs. 60 and 61). When radionuclides with little or no γ emission that produce better target/nontarget dose ratios are used, preliminary biodistribution studies must often be performed with other diagnostic radionuclides, and these studies are often radionuclide dependent. Alternatives which can be investigated include bremsstrahlung imaging or substituting a better y-emitting isotope of the same element. Unfortunately, scintigraphic resolution from bremsstrahlung may be poor, making quantitation for dosimetry difficult. Because of its high-energy beta particle, suitable half-life, good chelation properties and availability, several groups are currently studying the use of 9 0Y as a RIT labe1.62-64 Since 9 0Y is unsuitable for quantitative imaging, many 111 groups are utilizing In biodistribution data to predict 90 dose from Y administrations. However, even though there are similarities in tumor uptake, blood clearance, and other tissue uptakes, often there are substantial differences in retention and clearance from kidney and the reticuloendothelial system. For example, it was recently shown that although intravascular kinetics in patients are similar for 90 Y and 111 In labeled T101 antibody using isothiocyanatobenzyl DTPA, the two preparations differ in their tissue biodistribution. 65 Yttrium-88 is a suitable stand-in for studies in animals but it is not widely available and cannot be used in humans because of undesirable decay properties. Even though imaging photons in 186 Re can be used particularly at therapeutic dose levels 66,67 the “matched pair” 186 approach using 9 9 m Tc and Re, the former for imaging and the latter for therapy is a very attractive option. 6 7 These can both be attached to antibodies via similar c h e m i s t r y6 7 , 6 9 and generally produce similar biodistributions. Additionally, 109 Pd (Ref. 70) has also been investigated for immunotherapy. Although 1 0 9 Pd, 1 4 2 Pr, and 159 Gd all have half-lives of somewhat less than one day, they could be useful for MoAb or MoAb fragment systems that demonstrate a more rapid tumor uptake. Genetic engineering of antibodies with functionalities for binding of 99m gamma emitters (e.g., Tc) inserted into their structure may allow imaging with the same preparations prior to therapeutic administration of the beta emitter. 3 IV. RADIONUCLIDE PRODUCTION The criteria for the isotopes listed in Table I were the match between the radionuclide physical properties and the biological model used. Obviously, the possible production techniques and resultant specific activity must also be considered. In a reactor, uranium fission, radiative neutron capture and fast-neutron reactions can be employed. In accelerators, a wide range of particles (p,d,a, etc.) of varying energy is available. Table II gives recommended pro-

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duction routes for the various radionuclides of Table I. The nuclear reactions have acceptable cross sections for producing therapeutic quantities. There is a large range in the total activity and specific activity achievable for these radionuclides. For therapy, it is reasonable to assume that a minimum of 1.8 GBq will be required per treatment. It is more difficult to place a lower limit on the required specific activity. This depends on the chemical sensitivity of the particular antibody system to labeling conditions and on protein concentration requirements due to the presence of carrier. The availability and cost of the antibody becomes a factor, since larger amounts of antibody are required to bind enough radioactivity as well as the chemically identical cold atoms. This concern has become less critical recently as production techniques have improved and since many clinical protocols already use large (>50mg) amounts of antibody. A specific activity of approximately 100 GBq/mg will nonetheless be a highly desirable goal. Adequate quantity and quality of 131I are available commercially. Copper-67 is produced by high energy spallation reactions in the Brookhaven Linac Isotope Producer (BLIP) at Brookhaven National Laboratory” and the Los Alamos Meson Physics Facility (LAMPF) at Los Alamos National Laboratory and is available from these institutions most of the year. Although this is intrinsically a nocarrier-added method, ubiquitous trace Cu impurities limit achievable specific a c t i v i t y t o a p p r o x i m a t e l y 2 5 0 G B q / m g . 71,72 The fast neutron reaction on enriched 6 7Z n can be used to fill in the gaps in the operating schedules of the large accelerators. Large quantities of 1 5 3Sm can be produced very simply by thermal neutron activation because of its large cross section (σ= 208 barns) and epitherma1 resonance integral (3000 barns).73 A similar situation exists for 1 7 7Lu (σ=2100 barns). Nevertheless, adequate specific activity can probably only be achieved at nuclear reactors with neutron fluxes of greater than 3 x 10 14 n/cm2 s [e.g., the High Flux Beam Reactor (HFBR) at Medical Physics, Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

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Brookhaven National Laboratory, High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory, and U. Missouri Research Reactor]. With a neutron capture crosssection of 111 barns, 194 Ir production is not as attractive as 153 Sm and 1 7 7 Lu but still feasible at the above reactors. Samarium and lutetium are rare earth elements which can be readily chelated for linkage to antibodies. However, the in vivo stability of these preparations will need to be carefully investigated due to the high affinity of these metals for bone and the well-known tendency of rare earth elements to form colloids in vivo and thence concentrate in the reticuloendothelial system including bone marrow. There are two possible routes for the production of 199 Au. The double neutron capture reaction on natural gold leads to high yield because of the enormous cross section of 198 Au (26000 barns), but the specific activity is inadequate for RIT. Thus the indirect reaction on 198Pt f o l l o w e d b y β d e c a y t o 1 9 9A u h a s r e c e n t l y b e e n investigated 54,74 and appears to be practical. A similar method for 1 0 5 Rh can be used. For both these radionuclides, production at a high flux reactor will be advantageous. Rhenium-188 is especially interesting because it can be prepared in high specific activity from a convenient 188 W /1 8 8 R e g e n e r a t o r s y s t e m . T h e 1 8 8 W /1 8 8 R e s y s t e m could be considered a therapeutic analog to the 99 M o /9 9 m Tc generator since the chemistry of rhenium in many ways is similar to that of technetium. 68,69 Unfortunately the 188W parent can only be produced in low specific activity by a double neutron capture reaction, which limits the total activity of 188 W that can be loaded on an alumina column.” A gel-type generator partially overcomes this limitation. 7 6 One of the most widely used radionuclides is actually produced via a generator system, i.e., 90Sr/90Y. This allows repeated use of the 9 0Y for a lifetime since the half-life of 90 Sr is 29 years; a great convenience. The 9 0Sr/9 0Y generator (e.g., Refs. 77 and 78), is not available commercially as a system but 90Y alone can be purchased commercially. Without any gamma emissions, in vivo biodistribution studies remain a problem. Also, the in vivo stability of earlier DTPA-based chelates for use with 9 0Y is not o p t i m u m . 7 9 , 8 0 Recent studies with macrocyclic ligands 81-83 and certain carbon backbone substituted DTPA ligands, 8 4 however, show enhanced stability in serum and improved biodistribution. The safety of research personnel is a concern with 90Sr because of its high toxicity. The high energy beta emission, long life, and propensity to concentrate in bone make the maximum permissible body burden of 9 0S r only 2 µCi. Further, contamination monitoring for 9 0S r and 9 0Y are complicated due to the lack of gamma emissions. Rhenium-186 is an attractive alternative but requires a high flux reactor to achieve adequate specific activity. Therapeutic quantities of “As may be quite difficult to produce because of the instability of selenide targets at high beam current. Various alloy targets have been developed 85 but can be used only up to 20 µA. Additionally, existing chelation methods are not suitable for attaching arsenic to MoAbs. The production of large quantities

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o f 1 0 9Pd is straightforward, but with a specific activity at the lower end of this compilation. Since this may not be a serious problem in the future, its ease of production and favorable labeling chemistry” make it a possible candidate for RIT. The remaining entries in Table II are rare earth elements and would be expected to have chemical behavior similar to 153Sm. There are two possible reactions to make 142 Pr, offering either high yield or high specific activity, a situation analogous to 199 Au. Promethium-149, 166 Ho, and 159 Gd could be produced in adequate yield and high specific activity and so are also reasonable candidates. ACKNOWLEDGMENTS We would like to acknowledge the valuable discussions and critical review contributed by E. D. Yorke and B. W. Wessels. The comments of D. J. Buchsbaum, K. E. Britton, J. Humm, and W. A. Volkert were also helpful in the preparation of this manuscript. This work was supported by the Office of Health and Environmental Research, U.S. Department of Energy, under Contract No. DE-AC0276CH00016. Thanks are due to Ms. S. Cataldo for help with the preparation of this manuscript. 1

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ment of a stable radioiodinating reagent to label monoclonal antibodies for radiotherapy of cancer,” J. Nucl. Med. 30. 216-226 (1989). 58 L. A. Khawli and A. I. Kassis. “Synthesis of 125 I labeled N-succinimidyl p-iodobenzoate for use in radiolabeling antibodies,” Nucl. Med. Biol. 16, 727-733 (1989). 59 G. Vaidyanathan and M. R. Zalutsky, “Protein radiohalogenation observations on the design of N-succinimidyl ester acylation agents,” Bioconjugate Chem. 1, 269-273 (1990). 60 J. F. Eary. O. W. Press, C. C. Badger, L. D. Durack. K. Y. Richter, S. J. Addison, K. A. Krohn. D. R. Fisher, B. A. Porter, D. L. Williams, P. J. Martin, F. R. Appelbaum, R. Levy, S. L. Brown, R. A. Miller, W. B. Nelp, and I. D. Bernstein. “Imaging and treatment of B-cell lymphoma.” J. Nucl. Med. 31. 1257-1268 (1990). 61 S. M. Larson, A. Raubitschek. J. C. Reynolds, R. D. Neumann, K. Erik-Hellstrom, I Hellstrom, D. Colcher, J. Schlom, E. Glatstein, and J. A. Carrasquillo, “Comparison of bone marrow dosimetry and toxic 131 effect of high dose I-labeled monoclonal antibodies administered to man.” Nucl. Med. Biol. 16, 153-158 (1989). 62 L. C. Washburn, T. T. Hwa Sun, J. E. Crook, B. L. Byrd, J. E. Carlton, Y. W. Hung, and Z. S. Steplewski. “Y-90-labeled monoclonal antibodies for cancer therapy,” Nucl. Med. Biol. 13, 453-456 (1986). 63 S. E. Order, J. L. Klein, P. K. Leichner, J. Frinke, C. Lollo, and J. Carlo, “Yttrium-90 antiferritin. A new therapeutic radiolabeled antibody,” Int. J. Radiat. Oncol. Biol. Phys. 12, 227-281 (1986). 64 D. J. Hnatowitch, M. Chinol, D. A. Siebecker, M. Gionet, T. Griffin, P. W. Doherty, R. Hunter, and K. R. Kase, “Patient biodistribution of intraperitoneally administered yttrium-90 labeled antibody,” J. Nucl. Med. 29, 1428-1435 (1988). 65 J. A. Carrasquillo, B. Kramer, T. Fleisher, P. Perentesis, C. J. Boland, F. Foss, M. Rotman, J. C. Reynolds, J. L. Mulshine, L. Camera, J. Frincke, C. Lollo, R. D. Neumann, S. M. Larson, and A. Raubitschek, “In-111 versus Y-90 T101 biodistribution in patients with hematopoietic malignancies,” J. Nucl. Med. 32, 970 (1991) (abstract). 66 J. F. Eary, L. Durak, D. Williams, and J-L. Vanderheyden, “Considerations for imaging Re-188 and Re-186 isotopes,” Clin. Nucl. Med. 15, 911-916 (1990). 67 H. B. Breitz, P. L. Weiden, J-L Vanderheyden, J. W. Appelbaum, M. J. Bjorn, M. F. Fer, S. B. Wolf, B. A. Ratliff, C. A. Seiler, D. C. Foisie, D. R. Fisher, R. W. Schroff, A. R. Fritzberg, and P. G. Abrams, “Clinical experience with rhenium-186-labeled monoclonal antibodies for radioimmunotherapy: Results of phase I trials,” J. Nucl. Med. 33, 1099-1112 (1992). 68 S. M. Quadri and B. W. Wessels, “Radiolabeled biomolecules with Re- 186: Potential for radioimmunotherapy,” Nucl. Med. Biol. 13, 447451 (1986). 69 H. Breitz, B. Ratliff, R. Schroff, J. L. Vanderheyden, A. Fritzberg, J. Appelbaum, D. R. Fisher, P. Abrams, and P. Weiden, “Phase I studies of 186Re whole MoAb and F(ab’)2 fragment for radioimmunotherapy in solid tumors,” J. Nucl. Med. 31, 724-725 ( 1990). 70 R. A. Fawwaz, T. S. T. Wang, S. C. Srivastava, J. M. Rosen, S. Ferrone, M. A. Hardy, and P. O. Alderson, “Potential of Pd-109-labeled antimelanoma monoclonal antibody for tumor therapy,” J. Nucl. Med. 25, 796-799 (1984). 71 A. K. DasGupta, L. F. Mausner, and S. C. Srivastava, “A new separation procedure for Cu from proton irradiated Zn,” Int. J. Appl. Radiat. Isot. 42, 371-376 (1991). 72 D. W. McPherson, T. W. Lee, and F. F. Knapp, “A simple colorimettic method for determination of the specific activity of spallation produced copper-67 using phenylglyoxal (PG) bis-(4N-methyl) thiosemicarbazone (TSC) derivatives,” Int. J. Appl. Radiat. Isot. 41, 689-692 (1990). 73 Chart of the Nuclides (Knoll Atomic Power Lab., General Electric Co., San Jose, CA, 1988), 14th ed. 74 K. L. Kolsky,199L. F. Mausner, J. F. Hainfeld. G. E. Meinken, and S. C. Srivastava, “ Au production for use as a radiolabel of gold cluster immunoconjugates,” J. Label. Compds. Radiopharm. 30, 211-213 (1990). 75 A. P. Callahan, D. E. Rice, and F. F.188Knapp, “ 188Re for therapeutic 188 applications from an alumina-based W/ Re radionuclide generator,” Nucl. Compact. 1, 3-5 (1989). 76 G. J. Ehrhardt, A. R. Ketring, T. A. Turpin, M. S. Razavi, J. L. Vanderheyden, F. M. Su, and A. R. Fritzberg, , “A convenient 188 W/188188 Re generator for therapeutic applications using low specific activity W,” in Technetium and Rhenium in Chemistry and Nuclear

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MIRDformulation Evelyn E. Watson and Michael G. Stabin Oak Ridge Institute for Science and Education, Oak Ridge, Tennessee 37831 Jeffry A. Siegel Cooper Hospital, Camden, New Jersey 08103 (Received 18 March 1992; accepted for publication 15 September 1992)

The Medical Internal Radiation Dose (MIRD) Committee of the Society of Nuclear Medicine has provided guidance on methods for calculating radiation absorbed dose estimates since 1968. The MIRD Primer 1 gives a complete explanation of the schema which is a series of general equations adaptable for use with either simple or complex anatomical and kinetic models. By definition, the absorbed dose is the energy absorbed from ionizing radiation per unit mass of tissue. Because absorbed dose from internally distributed radionuclides is never completely uniform,’ the MIRD equations give the average, or mean, absorbed dose to a volume of tissue. The schema is useful for estimating absorbed dose to volumes as small as a cluster of cells or as large as the total body. Microdosimetric techniques that account for statistical aspects of particle track structures and energy distribution patterns in microscopic volumes can be used to express energy deposition in tissues from materials labeled with alpha-particle or Auger-electron emitters, particularly those incorporated within cells. The equation for calculating the absorbed dose may be written in various forms depending on available information. An example is shown in Eq. (1):

where D(rk ← r h ) is the mean absorbed dose in-a target region r k from activity in a source region r h , Ah is the cumulated activity (time integral of activity over the time interval of interest) in the source, ∆ ι is the mean energy emitted by a radionuclide per nuclear transition, φ i ( rk ← rh) is the absorbed fraction (fraction of energy emitted in region rh that is absorbed in region r k ), and mk is the mass of the target r k . The absorbed fraction divided by the mass may be represented by Φ (rk ← r h ), the specific absorbed fraction. The total mean absorbed dose in a target region is calculated by summing the doses from all source regions to the target. Equation ( 1) can be divided into two types of parameters-physical and biological. I. PHYSICAL PARAMETERS A. Mean energy emitted per transition (A) The most readily obtainable and the most accurate values required for dose calculation are probably those related to the energy emitted from a radioactive source. Each type of radiation emitted by a radionuclide is characterized by its own mean energy per particle E i and its own intensity or number of particles emitted per transition n i. The mean 511

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energy emitted per transition ∆ i is equal to k ni E i where k is a constant that depends on the units used for the terms in Eq. (1). The Brookhaven National Laboratory maintains a file of decay information that can be used to determine the intensities and energies of the different emissions associated with the transformation of any known radionuclide. In 1989, the MIRD Committee published this information on 242 radionuclides in a form that can be easily used for dose calculation.* In addition to intensities and energies, delta (A) values are given in both traditional (rad g/µCi h) and SI (Gy kg/Bq s) units. Diagrammatic decay schemes are provided along with the physical halflives, daughter products, and other related data.

B. Absorbed fraction (φ) The absorbed fraction varies with the type and energy of the radiation, the type of material through which the radiation passes, and the geometric configuration and the composition of the source and the target. Its value cannot be less than 0 or greater than 1. For convenience in estimating absorbed fractions, radiation types are sometimes classified as penetrating and nonpenetrating. If the amount of energy imparted to any target other than the source is so insignificant as to have little effect on the absorbed dose, the radiation is considered to be nonpenetrating. The absorbed fraction in the source is equal to one, and absorbed fractions for all other targets are zero. The classification of radiation as penetrating or nonpenetrating is determined by the absorption properties of the radiation, the nature of the model describing the source and target, and the type of calculation. Radiations may be considered nonpenetrating in the calculation of mean absorbed dose to a source volume but penetrating when the spatial distribution of absorbed dose is required, such as in tumor dosimetry. Several techniques have been used to calculate absorbed fractions, such as Monte Carlo and buildup factor methods. 3-8 Software for determining energy deposition in tissue include the ALGAMP code which has been used to calculate absorbed fractions for humans at various ages and the Electron Gamma Shower package, commonly called EGS4, which is particularly useful for calculating the spatial distribution of absorbed dose from electrons and beta particles. In some instances, the reciprocity principle’ has been applied when absorbed fractions could not be calculated to the desired level of accuracy by other techniques. Symbolically, the reciprocity relationship can be illustrated as follows:

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Watson, Stabin, and Siegel: MIRD formulation

Frequently specific absorbed fractions Φ ( rk ← r h ), or φ ( rk ← r h)/m k, are calculated rather than absorbed fractions. By reciprocity, Absorbed fractions and specific absorbed fractions for photons in organs of a 70-kg Reference Man have been published by the MIRD Committee. 3,4 The committee has also provided absorbed fractions for photons in spheres, cylinders, and ellipsoids from one gram to 200 kg in mass. 5,6 In MIRD Pamphlet No. 7,8 Berger provided information on absorbed dose distributions around point sources that can be used in calculating specific absorbed fractions from beta particles and electrons. Leichner et al.9 developed a generalized, empirical point-source function for calculating absorbed doses in tumors from beta particles based on Berger’s tabulated absorbed-dose distributions. 8 C. Mean dose per unit cumulated activity (S) The product of ∆ and Φ is a constant for a given radionuclide and a given source-target combination, a value designated by the MIRD Committee as the S value. The mean absorbed dose equation can thus be written as (3) where S(rk ← r h ) = Σ ι∆ ιΦ ι ( rk + rh ). Values Of S have been published in MIRD Pamphlet No. 11 10 for a mathematical model representing an adult male (Reference Man) with most of the important organs. Absorbed fractions and specific absorbed fractions for other mathematical models can be used to calculate S values as needed. Cristy and Eckerman11 have developed models and calculated specific absorbed fractions from internal photon sources for Reference Woman (also used to represent a 15-yr-old male) as well as a 10-yr-old, a 5-yr-old, a 1-yr-old, and a newborn child. Mathematical descriptions of organs and regions of the body have been designed to supplement or improve those included in the original models. Of particular interest for monoclonal antibody dosimetry are models of the blood vessels12,13 and the peritoneal cavity. 1 4 Absorbed fractions and S values have also been calculated for small or irregularly shaped structures in the b o d y ? ‘ * Johnson et al. determined the radiation dose from 1 6 6 H o , 1 8 6 Re and 1 5 3 Sm at a bone-to-marrow interface using the EGS4 code and including the contribution of backscattered radiation to the marrow dose. 15 H u m m1 6 calculated absorbed fractions and dose rates for solid tumors with “cold-regions” surrounded by uniform distribution of radiolabeled monoclonal antibodies to illustrate the absorbed dose-rate profile for different radionuclides. Howell et al. 17 published dose-rate profiles for 3 2P, 6 7Cu. 9 0Y , 111 AG, 1 3 1I, 1 8 8Re, and 1 9 3 mPt in spherical “tumors” with radii of 0.05 and 0.5 cm. Akabani et al. have published beta absorbed fractions for a large number of radionuclides in spheres with radii ranging from 0.1-2.0 cm (Ref. 18). Most absorbed dose calculations are based on the assumption that the absorbed fractions and the mass of the target remain constant during the time of irradiation. This Medical Physics. Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

is not always the situation. Howell et al. have studied changes in absorbed dose for rapidly growing tumors.” In radionuclide therapy, the volumes of the tumors may change greatly during the period over which the dose is delivered. Folding the tumor masses into the calculation may result in more accurate doses and a more meaningful determination of the dose-response relationships. Several investigators have calculated absorbed fractions for cellular configurations.20-22 A few examples will suffice to illustrate this. Kassis et al. determined absorbed fractions and absorbed dose rates to cells for nuclear transitions occurring inside the cell, in other cells, and in the extracellular medium.20 Makrigiorgos et al. 21 used this technique to calculate absorbed doses for cell clusters with different cellular diameters and different fractions of the cell volume that are labeled. Bardies and Myers have presented a model for cellular and cell cluster dosimetry for use in targeted radionuclide therapy. 22 Some of these models have been proposed as evidence of the limitations of the MIRD technique; however, the components of the calculations are the same as those in the MIRD schema. For example, the absorbed dose may be given as a function of distance along a defined axis, but the calculation is based on absorbed fractions or specific absorbed fractions defined as a function of distance along the axis. II. BIOLOGICAL PARAMETERS A. Cumulated activity (A) The cumulated activity A h represents the total number of nuclear transformations occurring during the time of interest in the source region r h and may be expressed in units of microcurie hours, Becquerel seconds, or an appropriate multiple of these units. A compilation of cumulated activities for various radionuclides or radioactive compounds has not been published by the MIRD Committee because the source regions differ for each radiolabeled material, and the source regions and their cumulated activities often change as new research results become available. The residence time τ of a radionuclide in a source region is equal to the cumulated activity in the source divided by the administered activity; that is (4) Although activity can sometimes be measured directly by external measurements with a scintillation camera in either the planar or SPECT modes, cumulated activities and residence times are not always available because of difficulties in directly measuring the activity in organs or regions of the body. Frequently, these values are determined indirectly through measurements that can be made, such as total body retention, excretion, blood clearance, etc., and the use of compartmental analysis techniques. 23 Computer software has been developed that permits the application of compartmental analysis to the development of models that will yield residence times in the organs or regions of interest. One such program is the Simulation, Analysis, and Modeling (SAAM) program.24 This software is available without cost from the Resource Facility for Kinetic Anal-

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ysis, Center for Bioengineering, FL-20, University of Washington, Seattle, WA 98195. Versions of the software are available for use on several computers such as the VAX, IBM-compatible personal computers, and many others. Although data collected in humans are always preferable, data collected in animals may sometimes be extrapolated to give estimates of the time-activity behavior of a radionuclide in humans.2 5 No single technique for such extrapolation has been generally accepted; however, great care must be taken in collecting the data and in performing the extrapolation to assure that these extrapolations are performed as accurately as possible. 26 Data should be presented in a manner that will allow other investigators to make use of the information and possibly recalculate if better extrapolation techniques are determined. The MIRD Committee has published 15 dose estimate reports 1,27-29 for nuclear medicine radiopharmaceuticals. Each report includes the biological models used for calculating cumulated activities needed for the dose estimate. These models can sometimes be adapted for other situations and other radionuclides. They also can be useful in determining how models may be developed and how data should be collected. III. EXTENSION OF MIRD SCHEMA TO MONOCLONAL ANTIBODY DOSIMETRY The MIRD schema is accepted as a useful technique for estimating the radiation dose from radioactive material within the human body. With respect to the dosimetry of radiolabeled antibodies, the MIRD Committee has provided a description of the ingredients that produce an absorbed dose estimate. The basic equations are applicable to tissues of various sizes and shapes and in different geometric relationships with each other. The committee has published data for calculating the mean absorbed dose in targets from activity that can be considered to be uniformly distributed in source organs or in small spheres and ellipsoids. 3-7 Absorbed fractions or specific absorbed fractions for nonuniform activity distributions or for nonstandard geometries will need to be calculated for some situations. Investigators have already generated absorbed fractions and specific absorbed fractions of energy from alpha and beta particles and electrons for some spherical tumors at the macroscopic or millimeter level 16-18 and for nonuniform distribution within cell clusters. 20-22 Such values are not usually required for photon radiations. Autoradiographic studies have clearly shown nonuniform distribution of radiolabeled monoclonal antibodies in tumors. The MIRD schema can be used to estimate absorbed doses for nonuniform distributions if the necessary data are obtained. The limitation is in the lack of an adequate model rather than in the schema. As the volume for which the absorbed dose is calculated becomes smaller, the nonuniformity of dose within that volume also becomes smaller. From the standpoint of absorbed dose, localization of activity in individual structures of a cell or in parts of a Medical Physics. Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

tumor mass is analogous to localization of activity in organs of the body. The greatest obstacles to estimating absorbed doses for radiotherapy agents are the measurement of activity distributions over time and the assessment of geometric relationships among sources and targets within the tissue. Calculating residence times or cumulated activities is not difficult if necessary biological data are obtained, and computer software is available to calculate absorbed fractions of energy if the tissue volumes of interest are defined. A possible technique for circumventing these problems may be to calculate a range of doses as well as a mean absorbed dose for a region as presented by Roberson et al. 30 for radiolabeled microsphere therapy. This gives an estimate of the variations in absorbed dose that exist in regions where the activity distributions are significantly nonuniform.

IV. SUMMARY The MIRD schema is not restricted to calculating mean absorbed doses in organs but can be extended to any tissue for which distribution and retention data can be obtained and for which a reasonably accurate mathematical description of the source and target tissues can be determined. The development of more accurate absorbed dose estimates and the correlation of these estimates with radiation effects will lead to a better understanding of the results from radiotherapeutic agents such as radiolabeled monoclonal antibodies. Therefore, radiobiologists and internal dosimetrists need to combine their efforts and work toward the common goal of improving the treatment of malignant diseases.

1

R. Loevinger, T. F. Budinger, and E. E. Watson, MIRD Primer for Absorbed Dose Calculations (Society of Nuclear Medicine, New York, NY, 1988). 2 D. A. Weber, K. F. Eckerman, L. T. Dillman, and J. C. Ryman, MIRD: Radionuclide Data and Decay Schemes (Society of Nuclear Medicine, New York, NY, 1989). 3 W. S. Snyder, M. R. Ford, G. G. Warner, and H. L. Fisher, Jr., ‘Estimates of absorbed fractions for monoenergetic photon sources uniformly distributed in various organs of a heterogeneous phantom, MIRD Pamphlet No. 5,” J. Nucl. Med. 10, Suppl. 3 (1969). 4 W. S. Snyder, M. R. Ford, and G. G. Warner, Estimates of Specific Absorbed Fractions for Photon Sources Uniformly Distributed in Various Organs of a Heterogeneous Phantom, MIRD Pamphlet No. 5, Revised (Society of Nuclear Medicine, New York, NY, 1978). 5 G. L. Brownell, W. H. Ellett, and A. R. Reddy, “Absorbed fractions for photon dosimetry, MIRD Pamphlet No. 3,” J. Nucl. Med. 9, Suppl. No. 1, 27-39 (1968). 6 W. H. Ellett and R. M. Humes, “Absorbed fractions for small volumes containing photon-emitting radioactivity, MIRD Pamphlet No. 8,” J. Nucl. Med. 12, Suppl. No. 5, 25-32 ( 1971). 7 M. J. Berger, “Energy deposition in water by photons from point isotropic sources, MIRD Pamphlet No. 2,” J. Nucl. Med. 9, Suppl. No. 1, 15-25 (1968). 8 M. J. Berger, “Distribution of absorbed dose around point sources of electrons and beta particles in water and other media, MIRD Pamphlet No. 7,” J. Nucl. Med. 12, Suppl. No. 5, 1-23 (1971). 9 P. K. Leichner, W. G. Hawkins, and N.-C. Yang, “A generalized, empirical point-source function for beta-particle dosimetry,” Antib. Immunoconjug. Radiopharm. 2, 125-144 (1989).

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W. S. Snyder, M. R. Ford, G. G. Warner, and S. B. Watson, "S" Absorbed Dose Per Unit Cumulated Activity for Selected Radionuclides and Organs, MIRD Pamphlet No. 11 (Society of Nuclear Medicine, New York, NY, 1975). 11 M. Cristy and K. F. Eckerman, “Specific absorbed fractions of energy at various ages from internal photon sources,” ORNL/TM-8381, Vols. 1-7 (1987). 12 G. Akabani and J. W. Poston, Sr., “Absorbed dose calculations to blood and blood vessels for internally deposited radionuclides,” J. Nucl. Med. 32, 830-834 (1991). 13 R. E. Faw and J. K. Shultis, “Dosimetry calculations for concentric cylindrical source and target regions with application to blood vessels,” Health Phys. 62, 344-350 (1992). 14 E. Watson, M. G. Stabin, J. L. Davis, and K. F. Eckerman, “A model of the peritoneal cavity for use in internal dosimetry,” J. Nucl. Med. 30, 2002-2011 (1989). 15 J. C. Johnson, S. M. Langhorst, S. K. Loyalka, W. A. Volkert. and A. R. Ketring, “Calculation of radiation dose at a bone-to-marrow interface using Monte Carlo modeling techniques (EGS4),” J. Nucl. Med. 33, 623-628 (1992). 16 J. L. Humm, “Dosimetric aspects of radiolabeled antibodies for tumor therapy,” J. Nucl. Med. 27, 1490-1497 (1986). 17 R.W. Howell, D. V. Rao, and K. S. R. Sastry, “Macroscopic dosimetry for radioimmunotherapy: Nonuniform activity distributions in solid tumors,” Med. Phys. 16, 66-74 (1989). 18 G. Akabani, J. W. Poston, Sr., and W. E. Belch, “Estimates of beta absorbed fractions in small tissue volumes for selected radionuchdes.” J. Nucl. Med. 32, 835-839 (1991). 19 R. W. Howell, V. R. Narra, and D. V. Rao, “Absorbed dose calculations for rapidly growing tumors,” J. Nucl. Med. 33, 277-281 (1992). 20 A. I. Kassis, S. J. Adelstein, C. Haydock, and K. S. R. Sastry, “Thallium-201: An experimental and a theoretical radiobiological approach to dosimetry,” J. Nucl. Med. 24, 1164-1175 (1983). 21 G. M. Makrigiorgos, S. J. Adelstein, and A. I. Kassis, “Limitations of conventional internal dosimetry at the cellular level,” J. Nucl. Med. 30, 1856-1864 (1989). 22 M. Bardies and M. J. Myers, “Development and validation of a simple


514 model for cellular and ceil cluster dosimetry with practical application in targeted radionuclide therapy," in Fifth International Radiopharmaceutical Dosimetry Symposium, CONF-910529. edited by E. E. Watson and A. T. Schlafke-Stelson (Oak Ridge Associated Universities, Oak Ridge, TN, 1992), pp. 531-543. 23 M. Berman, Kinetic Models for Absorbed Dose Calculalions. MIRD Pamphlet No. 12 (Society of Nuclear Medicine, New York, NY, 1977). 24 M. Berman and M. F. Weiss, SAAM Manual (U.S. DHEW Publication No. (NIH) 78-108, US. Government Printing Office, Washington, DC, 1978). 25 H. D. Roedler, “Accuracy of internal dose calculations with special consideration of radiopharmaceutical biokinetics,” in Third International Radiopharmaceutical Dosimetry Symposium, edited by E. E. Watson, A. T. Schlafke-Stelson, J. L. Coffey, and R. J. Cloutier (Oak Ridge Associated Universities, Oak Ridge, TN, 1981), pp. I-20. 26 K.A. Lathrop,” Collection and presentation of animal data relating to internally distributed radionuclides,” Third International Radiopharmaceutical Dosimetry Symposium, edited by E. E. Watson, A. T. Schlafke-Stelson, J. L. Coffey, and R. J. Cloutier (Oak Ridge Associated Universities, Oak Ridge, TN, 1981). pp. 198-203. 27 D. A. Weber, P. Todd Makler, Jr., E. E. Watson, J. L. Coffey, S. R. Thomas, and J. London, “MIRD Dose Estimate Report No. 13. Radiation absorbed dose from technetium-99m-labeled bone imaging agents,” J. Nucl. Med. 30, 1117-I 122 (1989). 28 H. L. Atkins, S. R. Thomas, U. Buddemeyer, and L. R. Chervu, “MIRD Dose Estimate Report No. 14. Radiation absorbed dose from technetium-99 m-labeled red blood cells,” J. Nucl. Med. 31, 378-380 (1990). 29 J.S. Robertson, M. D. Exekowitz, M. K. Dewanjee, M. G. Lotter, and E. E. Watson, “MIRD Dose Estimate Report No. 15. Radiation absorbed dose for radioindium-labeled autologous platelets,” J. Nucl. Med. 33, 777-780 (1992). 30 P. L. Roberson, R. K. Ten Haken, D. L. McShan, P. E. McKeever, and W. D. Ensminger, “Threedimensional tumor dosimetry for hepatic yttrium-90-microsphere therapy,” J. Nucl. Med. 33, 735-738 (1992).

Pharmacokinetic modeling Sven-Erik Strand Department of Radiation Physics, Lund University, University Hospital, S-221 85, Lund, Sweden Pat Zanzonico Division of Nuclear Medicine. New York Hospital-Cornell Medical Center, New York. New York Timothy K. Johnson Department of Radiology. University of Colorado, Denver, Colorado (Received 18 March 1992; accepted for publication 27 November 1992) For radiation dosimetry calculations of radiolabeled monoclonal antibodies, (MAb), pharmacokinetics are critical. Specifically, pharmacokinetic modeling is a useful component of estimation of cumulated activity in various source organs in the body. It is thus important to formulate general methods of pharmacokinetic modeling and of pharmacokinetic data reduction, leading to cumulated activities. In this paper different types of models are characterized as “empirical,” “analytical,” and “compartmental” pharmacokinetic models. There remains a pressing need for quantitative studies in man for a proper understanding of the pharmacokinetics of MAb. Pharmacokinetic modeling of radiolabeled MAb in vivo has relied on relatively limited studies in man and complementary detailed measurements in animals. In either case, any model chosen for analysis of such data is inevitably based on measurements of limited accuracy and precision as well as assumptions regarding human physiology. Very few macroscopic compartmental pharmacokinetic models for MAb, have been tested over a range of conditions to determine their predictive ability. Extracorporeal immunoadsorption represents one approach for drastically altering the biokinetics of antibody distribution, and may serve to validate a given pharmacokinetic model. In addition to macroscopic modeling, the microscopic evaluation of the timedependent distribution of radiolabeled MAb in tissues is of utmost importance for a proper understanding of the kinetics and radiobiologic effect. Many tumors do not exhibit homogeneous uptake. A mathematical understanding of that distribution is thus essential for accurate tumor dosimetry estimates. This review summarizes methodologies for pharmacokinetic modeling, critically reviews specific pharmacokinetic models and demonstrates the capability of modeling for predictive calculations of altered pharmacokinetics, emphasizing its use in dosimetric calculations.

1. INTRODUCTION Epitomizing Ehrlich’s century-old conceptualization of the “magic bullet,” radiolabeled monoclonal antibodies (MAb) against tumor-specific and/or associated antigens have spurred an unprecedented worldwide effort in nuclear medicine research. A sound quantitative understanding of the pharmacokinetics and thus a systematic approach to the radiation dosimetry of these target tissue-specific radiopharmaceuticals has largely remained elusive, however. Indeed, the general difficulties inherent in generating reasonably accurate and precise cumulated activity and absorbed dose estimates for internal radionuclides are exacerbated for radiolabeled MAb because of the marked qualitative as well as quantitative differences in their pharmacokinetics among different species, different individuals, different antibodies, different radionuclides, different modes of administration, and different administered amounts. Accordingly, radiation dosimetry of sufficient accuracy and precision for therapeutic application of radiolabeled MAb, as dictated by the generally marginal therapeutic index (i.e., the tumor-to-critical normal tissue absorbed dose ratio), must be performed on an individualized basis. Thus the general treatment planning paradigm used, for 515

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example, in radioiodine treatment of metastatic thyroid cancer’ should be considered for radioimmunotherapy: a low-activity tracer administration, kinetic studies consisting of serial measurements of tissue activities, absorbed dose estimation and projection to the maximum “safe” and the minimum “therapeutically effective” administered activities, and a high-activity therapy administration (with additional kinetic studies for verification of the actual therapeutic absorbed doses). Nonetheless, practical quantitative radionuclide imaging methods including planar, single-photon emission computed tomography (SPECT), and positron emission tomography (PET), as well as probe-based organ and total. body activity measurements and ex vivo blood activity concentration measurements have been developed and published in detail; 1-36 the reader is referred to the pertinent contributions in this volume for additional information. II. PRACTICAL SIGNIFICANCE OF PHARMACOKINETIC MODELING Pharmacokinetic modeling is a useful component of estimation of cumulated activities (i.e., the number of nuclear transformations) in the various source regions of the body. Although a general concept in internal radionuclide

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radiation dosimetry, the precise meaning of “cumulated activity” will be illustrated using the formalism promulgated by the Medical Internal Radiation Dosimetry (MIRD) Committee, the International Commission on Radiation Units and Measurements (ICRU), and the International Commission on Radiological Protection ( I C R P ) . 3 8 - 5 1 The mean absorbed dose, D(r k ← r h ), to a target region, r k, from a radionuclide in a source region, r h, is given by the following equations: (1) and (2) where Ah is the cumulated activity (e.g., in Bq-h) in source region rh , Ah (t) is the radioactive decay-uncorrected activity (e.g., in Bq) in source region r h at time t p o s t administration (e.g., in h), and S(rk ← r h) is the “S factor” (e.g., in Gy/Bq-h) for target region r k and source region r h , that is, the absorbed dose to target region r k per unit cumulated activity in source region r h . Since there are generally multiple source regions, r h, for an internally distributed radionuclide, the total absorbed dose to the target region, r k , is given by the summation of the expression on the right side of Eq. ( 1) over all of the source regions, r h: (3) The S factor, S ( rk ← r h ), is a physical quantity related to the nuclear properties (i.e., the number, type, and energy of nuclear radiations and related emissions accompanying radioactive decay) of a particular radionuclide, the geometric orientation of and distance between the target region, r k , and the source region, r h , and the electron and mass densities, elemental composition, and effective atomic number of the target region, r k , the source region, r h , and the intervening tissues.” For specific anthropomorphic anatomic models (e.g., “Standard Man” 42,48 ), the values of S factors, S ( r k ← r h ), for many radionuclides and target region-source region pairs are tabulated and published. On the other hand, knowing the physical half-life of a radionuclide, the cumulated activities, A h , are biological quantities related to the pharmacokinetics of a particular radioactive material. In view of the practically infinite number of combinations of materials, radionuclides, physiological and pathological conditions, and amounts and modes of administration, it is obviously impractical to usefully tabulate pharmacokinetic parameters and/or cumulated activities of radioactive materials. It is therefore essential to formulate general methods of pharmacokinetic modeling and of pharmacokinetic data reduction leading to cumulated activities. III. TYPES OF PHARMACOKINETIC MODELS In the broadest sense, a pharmacokinetic model is simply a mathematical description of the distribution of some material over time. Although the following distinctions are Medical Physics, Vol. 20, No. 2. Pt. 2, Mar/Apr 1993

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neither rigorous nor standardized, it is didactically useful to separately consider the various types of pharmacokinetic models and their advantages and disadvantages. In radiation dosimetry practice, at least three general types of pharmacokinetic models can be identified: “empirical,” “analytic,” and “compartmental.” Whatever approach to pharmacokinetic modeling one adopts, the insightful admonition of Dr. Robert Loevinger should be borne very much in mind. 5 2 “It is never possible to calculate the dose to a patient; one can only calculate the dose to a model. The model, of course, is the totality of the assumptions necessary to make the calculation; these assumptions define a class of patients, and the dose applies to this class. How well a given patient fits the model is only conjectural...For internally distributed radionuclides, the models are crude, and the difference between the patient and model is vast...” A. Empirical pharmacokinetic models In applying radiotracer methodology, serial measurements of the amount or concentration of the radiotracer in one or more tissues are typically graphed as a function of time post-administration. (It is implicitly assumed that tissues of interest, including the target and/or critical organs, are, in fact, “measurable.“) The resulting time-activity curve itself may be characterized as an “empirical” pharmacokinetic model in that it is a mathematical description of the distribution of the radiotracer incorporating information derived only by direct measurement. If the activity measurements are not corrected for radioactive decay, then the area under the time-activity curve represents the timeintegral of the activity, that is, the cumulated activity [Eq. (2)]. The area under the time-activity curve may be evaluated by planimetry or some method of numeric integration (e.g., the trapezoidal rule, Simpson’s rule, etc.). However, the accuracy of such integration is highly dependent on judicious timing and adequate frequency of the measured data. An important advantage of empirical pharmacokinetic models is that no simplifying assumptions are introduced regarding the analytic form of the time-activity data or the biology of the radiotracer distribution. While it is difficult to measure the “zero-time” activity (in percent of administered activity) in a given tissue, one can reasonably equate this parameter with the percent of the total body volume of distribution of the radiotracer (e.g., plasma volume, extracellular water volume, etc.) contained in that tissue. It is also impossible to measure the activity or activity concentration indefinitely. It is therefore desirable but often impractical to include a sufficiently “late” final measurement (e.g., after five physical halflives, after the total body activity has decreased to less than 10% of the administered activity, etc.), to sufficiently minimize this source of error. Accordingly, one must generally assume that after the final measurement in a given tissue, its time-activity curve simply parallels that of the total body or there is no biological elimination (i.e., there is elimination only by radioactive decay in situ); this latter approach, which is used for blood and for the total body in

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the kinetic analysis of the low-activity tracer administration for planning radioiodine treatment of metastatic thyroid cancer,’ may result in overestimation of cumulated activities.

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function parameters [i.e., (Ah)j and (λ h )j ], related to the deviation of the measured time-activity curve from the fitted distribution function, q h (t). Incorporating the distribution function notation into the expression for the cumulated activity, A h , Eq. (3) can be reformulated as follows:

B. Analytic pharmacokinetic models In part to overcome the inability of empirical pharmacokinetic models to reasonably extrapolate beyond the generally limited time-activity data, one may fit these data to an analytic function (sometimes referred to as a “distribution function”). Implicit in such an “analytic” pharmacokinetic model is the assumption that the time-activity curve follows the fitted time-dependent function before the first measurement as well as after the final measurement. Since biological processes (such as the exchange of material among tissues) are generally assumed to follow first-order kinetics, time-activity curves are generally fit to a sum of exponentials (“by eye,” by exponential "curve stripping,” or, more commonly, by a computerized “least-squares” fitting algorithm5 3):

where q h (t) is the distribution function for source region r h, that is, the radioactive decay-corrected activity (e.g., in Bq) in source region r h at time t post-administration (e.g., in h) of the radiotracer, (Ah ) j is the activity (e.g., in Bq) for the jth exponential component in source region r h , at time t=0, and (λ h )j is the biological disappearance constant (e.g., in h-1) of the jth exponential component of the time-activity curve in source region r h, that is, the fraction of activity eliminated per unit time for the jth exponential component of the time-activity curve for source region r h . Time-activity data are generally plotted in semilogarithmic graphs, that is, the activity or activity concentration is plotted on a logarithmic ordinate scale versus the time on an arithmetic abscissa scale. In this way, each exponential component of the distribution function, q h (t), appears as a linear segment of the time-activity curve, and the number of exponential components corresponds to the identifiable number of linear segments. (If the “slopes” of the linear segments are not widely different, however, the resolution of the time-activity curve into distinct exponential components may be problematic). If the empirical time-activity curve is monotonically decreasing, the biological disappearance constants, (λ h)j, are negative (See Appendix I). In this case, the generally rising initial portion (i.e., the so-called “uptake phase”) of the time-activity curve has not been sampled and will not be accurately represented by the resulting distribution function, q h (t). If the empirical time-activity curve is more complex, consisting of both increasing and decreasing segments, the respective biological disappearance constants, (λ h), are positive and negative. Note that, in addition to the experimental error, or uncertainty, associated with each activity measurement, fitting the time-activity curve to an analytic function introduces an error in the estimated values of the Medical Physics, Vol. 20, No. 2, pt. 2, Mar/Apr 1993

where λ is the physical decay constant (e.g., in h - 1) of the radionuclide in the radiotracer, that is, the fraction of activity eliminated per unit time by radioactive decay. Substituting the expression for the distribution function, ( qh (t), in Eq. (4) into the expression for the cumulated activity, Ã h, in Eq. (5) and evaluating the resulting definite integral yields the following expression:

C. Compartmental pharmacokinetic models 1. General aspects An alternative, “physiological” approach to the determination of cumulated activities is based upon compartmental analysis,4 9 , 5 4 - 5 6 wherein a biological system is treated as an assortment of interconnected compartments each consisting of an ensemble of identical chemical or physical units. Each such ensemble is somehow localized in an identifiable anatomic entity (e.g., an organ such as the liver), an identifiable functional entity (e.g., the reticuloendothelial system), or an identifiable physical entity (e.g., the extracellular water space). Any such anatomically, functionally, or physically localized ensemble constitutes a “compartment.” Such an ensemble may not, however, actually be localized in any such identifiable entity and its existence as a discrete compartment is then purely conceptual. Normally, compartments tend to remain constant in terms of the size of the ensemble (i.e., the number of chemical or physical units), while undergoing continual turnover, by the net rate of input equaling the net rate of output. The existence of such a dynamic equilibrium, or “steady state,” the identifiability of specific compartments and the detectability of the flux of a non-perturbing tracer through various such compartments are implicit assumptions of compartmental analysis. A compartmental model is thus characterized by the number of compartments and by transition probabilities, or “exchange rates,” between compartments and may be represented mathematically by a set of coupled ordinary differential equations:

where dF(i,t)/dt is the flux of the tracer (e.g., in Bq/h through compartment i, that is, the net amount of tracer per unit time traversing compartment i, F(i,t),F(j,t) i s the amount of tracer (e.g., in Bq) in compartments i and j, respectively, at time t post-administration (e.g., in h), L(i,j,t),L(j,i,t) are the fractional exchange rates (e.g., in

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h -l) of the amount of tracer to compartment i from compartment j and to compartment j from compartment i, respectively, and n is the number of compartments in the model. The exchange rates, L(i,j,t) and L(j,i,t), are generally constant with time (i.e., time-invariant) and the flux of the tracer, dF(i,t)/dt, is generally a linear (i.e., first-order) function of the compartmental tracer contents, F(i,t) a n d F(j,t), yielding a set of coupled linear differential equations (i.e., a=b=1) and a so-called linear model.

When solved, the time-dependent amount of tracer in compartment i, F(i,t), is represented by a sum of exponentials.

2. MAb nonlinear compartment models In a compartmental model of systemically administered antibody, the finite antigen concentration and the resulting saturability of antigenic binding sites requires a non-linear compartmental model (i.e., a set of coupled differential equations including at least one non-linear differential equation), since the rates of association of the antigen and antibody and of dissociation of the antigen-antibody complex are not constant but dependent on the instantaneous concentrations of antigen, antibody, and antibody-antigen c o m p l e x .57,58 If “Ag,” “Ab,” and “AgAb” represent antigen, antibody, and antibody-antigen complex, respectively, then the antigen-antibody interaction can be represented by the following chemical reaction, characteristic of reversible bimolecular binding reactions:

w h e r e k+ 1 is the association rate constant (e.g., in h - 1 M -1), that is, the fractional amount of antibody binding to antigen per unit time per unit concentration of antigen and k -1 is the dissociation rate constant (e.g., in h - 1), that is, the fractional amount of antibody-antigen complex dissociating into free antigen and antibody per unit time. Accordingly, the gross rate of antibody binding to antigen to form the antibody-antigen complex and the gross rate of dissociation of the antibody-antigen complex to yield free antibody and antigen are given by Eqs. (10) and (11), respectively. (It is important to note that Eqs. (10) and (11) represent the gross, not the net [as is usually presented], binding and dissociation rates, respectively and presented to demonstrate the mathematical relationship between conventional antigen-antibody binding parameters and compartmental model exchange rates.):


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where [Ab] is the concentration (e.g., in M) of free antibody, [Ag] is the concentration (e.g., in M) of free antigen, and [AbAg] is the concentration (e.g., in M) of antibodyantigen complex. Equations (10) and (11) can be re-arranged to yield Eqs. (12) and (13), respectively, giving the fractional rates of antibody binding to antigen and of dissociation of the antibody-antigen complex:

If one now identifies a free antibody compartment and a bound antibody (i.e., an antibody-antigen complex) compartment, then the free antibody-to-bound antibody and the bound antibody-to-free antibody exchange rates are given, by definition, by Eqs. (12) and (13), respectively. Because the free antigen concentration is not constant, the free antibody-to-bound antibody exchange rate is not constant [Eq. (12)] and a nonlinearity is thereby introduced. Nonetheless, Eq. (11) can be reformulated entirely in terms of evaluable quantities to yield a time-varying expression for the gross free antibody-to-bound antibody exchange rate:

where [Ag] 0 is the total antigen concentration (e.g., in M) in the antigen-positive tissue, F[AbAg,t] is the amount of antibody (e.g., in mole) in the bound antibody compartment, and V d is the volume of distribution (e.g., in l) of the antibody in the antigen-positive tissue. (This may be approximated by the total volume or, preferably, the extracellular water volume of the antigen-positive tissue.) Note that if the amount of administered antibody is sufficiently small, the total concentration of antigen, [Ag] 0, will greatly exceed the concentration of antibody-antigen complex, [AbAg] = F(AbAg,t)/V d. It is mathematically obvious that the gross exchange rate of antibody binding to antigen is thus essentially constant and the overall compartmental model is thereby linearized. 3. Compartment model solution To “solve” a compartmental model, that is, to derive a compartmental model for which discrete values of the calculated compartmental contents, F(i,t), agree with the corresponding experimental data, within the respective uncertainty of each datum, the number of compartments and the values of the exchange rates, L(i,j,t), must be determined. There is actually no unique solution for a given set of experimental data since any compartmental model can be enlarged beyond the “resolution” possible from the data

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by the introduction of additional compartments (i.e., degrees of freedom). In practice, the ambiguity, or “nonuniqueness,” of compartmental model solutions is highly problematic because of the generally limited experimental data available in terms of both number of compartments sampled and the number and timing of data for each compartment. One generally adopts the compartmental model having the minimum number of compartments and consistent with the known relevant “biology,” subject to the following criteria: the “sum of squares” deviation between the calculated compartmental contents, F(i,t), and the corresponding experimental data should be minimized; the calculated compartmental contents, F(i,t), should be randomly, not systematically, dispersed about the corresponding experimental data; and the standard error of the parameter estimates should be reasonably small. 55,56 It is important to recognize, however, that the existence of compartmental model solution satisfying these criteria does not in itself constitute a “validation,” or proof, of a model. While difficult to define rigorously, validation of a compartmental model is related to its ability to qualitatively and quantitatively predict the biodistribution of a tracer in the system being modeled (i.e., yield calculated compartmental contents equal to the corresponding experimental data with the respective uncertainty of each datum) in response to a quantifiable perturbation of the system. An elegant example of such a quantifiable perturbation is extracorporeal immunoadsorption; its use in the validation of compartmental models of MAb is discussed below. The mathematical formalism for solving compartmental models, whether analytic or numeric (i.e., iterative), is formidable and, even for relatively simple models, outside the scope of this chapter; the reader is referred to Ref. 54-56. CONSAAM , an interactive, or “conversational,” version of Berman’s SAAM (simulation, analysis, and modeling) program is an extremely powerful, widely used, and fully supported compartmental modeling program. 5 7 The compartmental modeling-based calculation of cumulated activities can be performed by any number of methods. Solving the series of differential equations that define the model yield the model’s parameters (i.e., the amplitude and decay constant for each exponential term). Substitution of these parameters back into the defining differential equations, and integration from t=O to infinity, yield the cumulative activity specific to each source organ. Zanzonico et al.,58,59 have adapted the CONSAAM program to calculate the cumulated activity in source region r h , Ah , by introducing "virtual" compartments. For internal radionuclide dosimetry for MAb, Johnson has published a computer program, MABDOS .60 IV. PHYSIOLOGICAL CHARACTERISTICS OF MAb Antibody molecules are complex molecular structures, grouped into five distinct classes, IgG, IgA, IgM, IgE, and IgD. An IgG molecule has two long and two short amino acid chains called heavy and light chains, respectively. The molecular weight of MAb lies between 150000 and 900000 kDa for the intact antibody and between 50000 Medical Physics, Vol. 20, No. 2, Pt. 2, Mar/Apr 1993

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and 100000 kDa for the various fragments. The size is approximately 5-20 nm for intact antibody and l-3 nm for fragments. 61 To alter the biokinetics of the antibodies, the antibody molecule can be fragmented into Fab or F(ab’) 2 fragments. Many experimental and clinical reports have demonstrated low neoplastic-to-normal tissue activity uptake ratios. This may be due to the formation of antibody-antigen complexes, antibody metabolism in the reticuloendothelial system (RES), variability of antigen expression and limited access of antibodies to the tumor tissue. 62-66 Moreover complexes formed from the injected antibodies and host antibodies or circulating antigen will accumulate in the RES and the kidneys, although some reduction in circulating antigen can be obtained by plasmapheresis. 6 7 Many methods have been suggested to accelerate the clearance of residual circulating antibodies from the blood, including administration of second antibodies that will form complexes and be cleared by the RES. 68 A second approach is a two-stage method in which radiolabeled avidin is administered following the injection of a biotinylated administration of avidin-antibody a n t i b o d y6 9 o r conjugates. 7 0 - 7 2 V. TRANSPORT OF MACROMOLECULES INTO TISSUE The transport of antibody molecules into a tissue is governed by perfusion, microvascular permeability, interstitial transport, cell membrane permeability, concentration gradients, antigen concentration and antibody-antigen binding affinity. A summary of these factors and their implementation in pharmacokinetic modeling is given by Zanzonico et al.58 and Eger et al. 7 3 The Mab are transported via the blood stream or the lymph to tissues where they can cross the capillary endothelium to reach the interstitial fluid and thus to bind to cell-surface antigens. Capillary filtration depends not only upon the hydrostatic and colloid osmotic pressure, but on the endothelial wall porosity as well. The difference in capillary protein permeability approximately parallels the difference in filtration coefficient. The results from Ingvar et a1.74-76 confirm that so called “nonspecific binding” in organs is, to some extent, the result of capillary protein permeability and not to any active binding mechanism. This step is probably the most important factor in explaining why monoclonal antibodies do not achieve the high uptake ratios projected from in vitro experiments, Because of the size of the MAb and closed basement membrane of capillary endothelium in most normal tissues, penetration from the blood is very slow. The antibodies, however, have good access to liver (Kupffer cells), spleen and bone marrow because of fenestration of the basement membrane. The mean penetration time into extravascular space occurs with a half-life of the order of 10-50 h in normal tissue, whereas in solid tumors it is of the order of 10-20 h. The permeability, coupled with the possible expression of antigens on normal tissue, may limit tumor-tonormal tissue concentration ratios in vivo. However, Jain 77 noted that the neoplastic endothelium is much less struc-

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tured and has a higher probability of being more permeable to macromolecules than normal tissue endothelia. In the study of Covell et al. the transcapillary movement of antibodies was greatest in the lung, liver and spleen with the values 0.53, 0.35 and 0.20 ml min -1 g - 1, respectively. For other organs, the values are: kidney, 0.09, gut, 0.006, and carcass (skin, bone and muscle), 0.0003 m l m i n- 1 g - 1. A comparison was also made with other d a t a79 in which the transport of Dextrans with different molecular weights (equivalent Stoke’s radii for whole IgG and fragments) had been measured: Dextran (110000), 0.0023 ml/min and IgG, 0.0036 ml/min; Dextran (20000)) 0.0061 ml/min and F(ab’) 2, 0.0041 ml/min; and Dextran (10000), 0.029 ml/min and Fab’, 0.050 ml/min. The red bone marrow is characterized by large pores (