An image-based skeletal model for the ICRP reference adult male-specific absorbed fractions for neutron-generated recoil protons

Recoiling hydrogen nuclei are a principle mechanism for energy deposition from incident neutrons. For neutrons incident on the human skeleton, the small sizes of two contrasting media (trabecular bone and marrow) present unique problems due to a lack of charged-particle (protons) equilibrium. Specific absorbed fractions have been computed for protons originating in the human skeletal tissues for use in computing neutron dose response functions. The proton specific absorbed fractions were computed using a pathlength-based range-energy calculation in trabecular skeletal samples of a 40 year old male cadaver.

Methods for the inclusion of shallow marrow and adipose tissue in pathlength-based skeletal dosimetry

Distributions of linear pathlength measurements have been utilized in skeletal dosimetry of internally emitted short-range particles for over 30 years. This work reviews the methods for coupling these distributions to range-energy data. A revised methodology is presented for handling the insertion of the additional dosimetric target region (shallow marrow) and medium (adipose tissue) into the dosimetry algorithm. The methodology is shown to reduce the volume fraction of shallow marrow in the trabecular skeleton over existing methodologies. Finally, theoretical low and high-energy checkpoints are derived for use in checking the absorbed fraction and specific absorbed fraction results for a variety of source and target combinations.

Skeletal absorbed fractions for electrons in the adult male: considerations of a revised 50-microm definition of the bone endosteum

In 1995, the International Commission on Radiological Protection (ICRP) issued ICRP Publication 70 which provided an extensive update to the physiological and anatomical reference data for the skeleton of adults and children originally issued in ICRP Publication 23. Although ICRP Publication 70 has been a valuable document in the development of reference voxel computational phantoms, additional guidance is needed for dose assessment in the skeletal tissues beyond that given in ICRP Publication 30. In this study, a computed tomography (CT) and micro-CT-based model of the skeletal tissues is presented, which considers (1) a 50-microm depth in marrow for the osteoprogenitor cells, (2) electron escape from trabecular spongiosa to the surrounding cortical bone, (3) cortical bone to trabecular spongiosa cross-fire for electrons and (4) variations in specific absorbed fraction with changes in bone marrow cellularity for electrons. A representative data set is given for electron dosimetry in the craniofacial bones of the adult male.

Image segmentation of trabecular spongiosa by visual inspection of the gradient magnitude

Recent advances in physical models of skeletal dosimetry utilize high-resolution 3-dimensional microscopic computed tomography images of trabecular spongiosa. These images are coupled to radiation transport codes to assess energy deposition within active bone marrow and trabecular endosteum. These transport codes rely primarily on the segmentation of the spongiosa images into bone and marrow voxels. Image thresholding has been the segmentation of choice for bone sample images because of its extreme simplicity. However, the ability of the segmentation to reproduce the physical boundary between bone and marrow depends on the selection of the threshold value. Statistical models, as well as visual inspection of the image, have been employed extensively to determine the correct threshold. Both techniques are affected by partial volume effect and can provide unexpected results if performed without care. In this study, we propose a new technique to threshold trabecular spongiosa images based on visual inspection of the image gradient magnitude. We first show that the gradient magnitude of the image reaches a maximum along a surface that remains almost independent of partial volume effect and that is a good representation of the physical boundary between bone and marrow. A computer program was then developed to allow a user to compare the position of the iso-surface produced by a threshold with the gradient magnitude. The threshold that produces the iso-surface that best coincides with the maximum gradient is chosen. The technique was finally tested with a set of images of a true bone sample with different resolutions, as well as with three images of a cube of Duocell aluminium foam of known mass and density. Both tests demonstrate the ability of the gradient magnitude technique to retrieve sample volumes or media volume fractions with 1% accuracy at 30 microm voxel size.

Considerations of anthropometric, tissue volume, and tissue mass scaling for improved patient specificity of skeletal S values

It is generally acknowledged that reference man (70 kg in mass and 170 cm in height) does not adequately represent the stature and physical dimensions of many patients undergoing radionuclide therapy, and thus scaling of radionuclide S values is required for patient specificity. For electron and beta sources uniformly distributed within internal organs, the mean dose from self-irradiation is noted to scale inversely with organ mass, provided no escape of electron energy occurs at the organ boundaries. In the skeleton, this same scaling approach is further assumed to be correct for marrow dosimetry; nevertheless, difficulties in quantitative assessments of marrow mass in specific skeletal regions of the patient make this approach difficult to implement clinically. Instead, scaling of marrow dose is achieved using various anthropometric parameters that presumably scale in the same proportion. In this study, recently developed three-dimensional macrostructural transport models of the femoral head and humeral epiphysis in three individuals (51-year male, 82-year female, and 86-year female) are used to test the abilities of different anthropometric parameters (total body mass, body surface area, etc.) to properly scale radionuclide S values from reference man models. The radionuclides considered are 33P, 177Lu, 153Sm, 186Re, 89Sr, 166Ho, 32P, 188Re, and 90Y localized in either the active marrow or endosteal tissues of the bone trabeculae. S value scaling is additionally conducted in which the 51-year male subject is assigned as the reference individual; scaling parameters are then expanded to include tissue volumes and masses for both active marrow and skeletal spongiosa. The study concludes that, while no single anthropometric parameter emerges as a consistent scaler of reference man S values, lean body mass is indicated as an optimal scaler when the reference S values are based on 3D transport techniques. Furthermore, very exact patient-specific scaling of radionuclide S values can be achieved if measurements of spongiosa volume and marrow volume fraction (high-resolution CT with image segmentation) are known in both the patient and the reference individual at skeletal sites for which dose estimates are sought. However, the study indicates that measurements of the spongiosa volume alone may be sufficient for reasonable patient-specific scaling of S values for the majority of radionuclides of interest in internal-emitter therapy.

Voxel effects within digital images of trabecular bone and their consequences on chord-length distribution measurements

Chord-length distributions through the trabecular regions of the skeleton have been investigated since the early 1960s. These distributions have become important features for bone marrow dosimetry; as such, current models rely on the accuracy of their measurements. Recent techniques utilize nuclear magnetic resonance (NMR) microscopy to acquire 3D images of trabecular bone that are then used to measure 3D chord-length distributions by Monte Carlo methods. Previous studies have shown that two voxel effects largely affect the acquisition of these distributions within digital images. One is particularly pertinent as it dramatically changes the shape of the distribution and reduces its mean. An attempt was made to reduce this undesirable effect and good results were obtained for a single-sphere model using minimum acceptable chord (MAC) methods (Jokisch et al 2001 Med. Phys. 28 1493-504). The goal of the present work is to extend the study of these methods to more general models in order to better quantify their consequences. First, a mathematical model of a trabecular bone sample was used to test the usefulness of the MAC methods. The results showed that these methods were not efficient for this simulated bone model. These methods were further tested on a single voxelized sphere over a large range of voxel sizes. The results showed that the MAC methods are voxel-size dependent and overestimate the mean chord length for typical resolutions used with NMR microscopy. The study further suggests that bone and marrow chord-length distributions currently utilized in skeletal dosimetry models are most likely affected by voxel effects that yield values of mean chord length lower than their true values.

Skeletal dosimetry via NMR microscopy: investigations of sample reproducibility and signal source

Nuclear magnetic resonance microscopy has been used for several years as a means of quantifying the 3D microarchitecture of the cancellous regions of the skeleton. These studies were originally undertaken for the purpose of developing non-invasive techniques for the early detection of osteoporosis and other bone structural changes. Recently, nuclear magnetic resonance microscopy has also been used to acquire this same 3D data for the purpose of both (1) generating chord length data across bone trabeculae and marrow cavities and (2) generating 3D images for direct coupling to Monte Carlo radiation transport codes. In both cases, one is interested in the reproducibility of the dosimetric data obtained from nuclear magnetic resonance microscopy. In the first of two studies, a trabecular bone sample from the femoral head of a 51-y-old male cadaver was subjected to repeated image acquisition, image processing, image coupling, and radiation transport simulations. The resulting absorbed fractions at high electron energies (4 MeV) were shown to vary less than 4% among four different imaging sessions of the same sample. In a separate study, two femoral head samples were imaged under differing conditions of the NMR signal source. In the first case, the samples were imaged with intact marrow. These samples were then subjected to marrow digestion and immersed in Gd-doped water, which then filled the marrow cavities. Energy-dependent absorbed fraction profiles for both the marrow-intact and marrow-free samples showed essentially equivalent results. These studies thus provide encouragement that skeletal dosimetry models of improved patient specificity can be achieved via NMR microscopy in vivo.

Site-specific variability in trabecular bone dosimetry: considerations of energy loss to cortical bone

With continual advances in radionuclide therapies, increasing emphasis is being placed on improving the patient specificity of dose estimates to marrow tissues. While much work has been focused on determining patient-specific assessments of radionuclide uptake in the skeleton, few studies have been initiated to explore the individual variability of absorbed fraction data for electron and beta-particle sources in various skeletal sites. The most recent values of radionuclide S values used in clinical medicine continue to utilize a formalism in which electrons are transported under a trabecular bone geometry of infinite extent. No provisions are thus made for the fraction of energy lost to the cortical bone cortex of the skeletal site and its surrounding tissues. In the present study, NMR microscopy was performed on trabecular bone samples taken from the femoral head and humeral proximal epiphysis of three subjects: a 51-year male, an 82-year female, and an 86-year female. Following image segmentation and coupling to EGS4, electrons were transported within macrostructural models of the various skeletal sites that explicitly include the spatial extent of the spongiosa, as well as the thickness of the surrounding cortical bone. These energy-dependent profiles of absorbed fractions to marrow tissues were then compared to transport simulations made within an infinite region of spongiosa. Ratios of mean absorbed fraction, as weighted by the beta energy spectra, under both transport methodologies were then assembled for the radionuclides 32P and 90Y. These ratios indicate that corrections to existing radionuclide S values for 32P can vary by as much as 5% for the male, 6% for the 82-year female, and 8% for the 86-year female. For the higher-energy beta spectrum of 90Y, these same corrections can reach 8%, 10%, and 11%, respectively.

Beta-particle dosimetry of the trabecular skeleton using Monte Carlo transport within 3D digital images

Presently, skeletal dosimetry models utilized in clinical medicine simulate electron path lengths through skeletal regions based upon distributions of linear chords measured across bone trabeculae and marrow cavities. In this work, a human thoracic vertebra has been imaged via nuclear magnetic resonance (NMR) spectroscopy yielding a three-dimensional voxelized representation of this skeletal site. The image was then coupled to the radiation transport code EGS4 allowing for 3D tracing of electron paths within its true 3D structure. The macroscopic boundaries of the trabecular regions, as well as the cortex of cortical bone surrounding the bone site, were explicitly considered in the voxelized transport model. For the case of a thoracic vertebra, energy escape to the cortical bone became significant at source energies exceeding approximately 2 MeV. Chord-length distributions were acquired from the same NMR image, and subsequently used as input for a chord-based dosimetry model. Differences were observed in the absorbed fractions given by the chord-based model and the voxel transport model, suggesting that some of the input chord distributions for the chord-based models may not be accurate. Finally, this work shows that skeletal mass estimates can be made from the same NMR image in which particle transport is performed. This feature allows one to determine a skeletal S-value using absorbed fraction and mass data taken from the same anatomical tissue sample. The techniques developed in this work may be applied to a variety of skeletal sites, thus allowing for the development of skeletal dosimetry models at all skeletal sites for both males and females and as a function of subject age.

Chord distributions across 3D digital images of a human thoracic vertebra

Radiation dose estimates to the trabecular region of the skeleton are of primary importance due to recent advancements in nuclear medicine. Establishing methods for accurately calculating dose in these regions is difficult due to the complex microstructure of this anatomic site and the typical ranges of beta-particles in both bone and marrow tissues. At the present time, models of skeletal dosimetry used in clinical medicine rely upon measured distributions of straight-line path lengths (chord lengths) through bone and marrow regions. This work develops a new three-dimensional, digital method for acquiring these distributions within voxelized images. In addition, the study details the characteristics of measuring chord distributions within digital images and provides a methodology for avoiding undesirable pixel or voxel effects. The improved methodology has been applied to a digital image (acquired via NMR microscopy) of the trabecular region of a human thoracic vertebra. The resulting chord-length distributions across both bone trabeculae and bone marrow cavities were found to be in general agreement with those measured in other studies utilizing different methods. In addition, this study identified that bone and marrow space chord-length distributions are not statistically independent, a condition implicitly assumed within all current skeletal dosimetry models of electron transport. The study concludes that the use of NMR microscopy combined with the digital measurement techniques should be used to further expand the existing Reference Man database of trabecular chord distributions to permit the development of skeletal dosimetry models which are more age and gender specific.

Voxel size effects in three-dimensional nuclear magnetic resonance microscopy performed for trabecular bone dosimetry

An important problem in internal dosimetry is the assessment of energy deposition by beta particles within trabecular regions of the skeleton. Recent dosimetry methods for trabecular bone are based on Monte Carlo particle transport simulations within three-dimensional (3D) images of real human bone samples. Nuclear magnetic resonance (NMR) microscopy is a 3D imaging technique of choice due to the large signal differential between bone tissue and the water-filled marrow cavities. Image voxel sizes currently used in NMR microscopy are between 50 microm and 100 microm, but the images are time consuming to acquire and can only be performed at present for in vitro samples. It is therefore important to evaluate what resolution is best suitable in order to properly characterize the trabecular microstructure, to adequately predict the tissue dosimetry, and to minimize imaging time. In this work, a mathematical model of trabecular bone, composed of a distribution of spherical marrow cavities, was constructed. The mathematical model was subsequently voxelized with different voxel sizes (16 microm to 1,000 microm) to simulate 3D NMR images. For each image, voxels are assigned to either bone or marrow according to their enclosed marrow fraction. Next, the images are coupled to the EGS4 electron transport code and absorbed fractions to bone and marrow are calculated for a marrow source of monoenergetic electrons. Radionuclide S values are also determined for the voxelized images with results compared to data calculated for the pure mathematical sample. The comparison shows that for higher energy electrons (>400 keV), good convergence of the results is seen even within images of poor resolution. Above 400 keV, a voxel resolution as large as 300 microm results in dosimetry errors below 5%. For low-energy electrons and high-resolution images, the self-dose to marrow is also determined to within 5% accuracy. Nevertheless, increased voxelization of the image overestimates the surface area of the bone-marrow interface leading to errors in the cross-dose to bone as high as 25% for some low-energy beta emitters.

A three-dimensional transport model for determining absorbed fractions of energy for electrons within trabecular bone

Bone marrow is generally the dose-limiting organ of concern in radioimmunotherapy and in radionuclide palliation of bone pain. However, skeletal dosimetry is complicated by the intricate nature of its microstructure, which can vary greatly throughout skeletal regions. In this article, a new three-dimensional electron transport model for trabecular bone is introduced, based on Monte Carlo transport and on bone microstructure information for several trabecular bone sites.

METHODS

Marrow cavity and trabecular chord length distributions originally published by Spiers et al. were randomly sampled to create alternating regions of bone, endosteum and marrow during the three-dimensional transport of single electrons. For the marrow spaces, explicit consideration of the site-specific elemental composition was made in the transport calculations based on the percentage of active and inactive marrow in each region. The electron transport was performed with the EGS4 electron transport code and the parameter reduced electron-step transport algorithm. Electron absorbed fractions of energy were tabulated for seven adult trabecular bone sites, considering three source and target regions: the trabecular marrow space (TMS), the trabecular bone endosteum (TBE) and the trabecular bone volume (TBV).

RESULTS

For all source-target combinations, the absorbed fraction was seen to vary widely within the skeleton. These variations can be directly attributed to the differences in the trabecular microstructure of the different skeletal regions. For many source-target combinations, substantial energy dependence was seen in the calculated absorbed fraction, a factor not considered in values recommended by the International Commission on Radiological Protection (ICRP). A one-dimensional model of electron transport in trabecular bone, based on range-energy relationships, was also developed to verify the three-dimensional transport model and to evaluate differences between the two modeling approaches. Differences of approximately 10%-15% were seen, particularly at low electron energies. In the case of a TBV source and a TMS target (or vice versa), differences >50% were seen in the absorbed fraction.

CONCLUSION

The three-dimensional model of electron transport in trabecular bone allows improved estimates of skeletal absorbed fractions. The model highlights both the regional and the energy dependency of the absorbed fraction not previously considered in the ICRP model.

NMR microscopy of trabecular bone and its role in skeletal dosimetry

One of the more intractable problems in internal dosimetry is the assessment of energy deposition by alpha and beta particles within trabecular, or cancellous, bone. In the past few years, new technologies have emerged that allow for the direct and nondestructive 3D imaging of trabecular bone with sufficient spatial resolution to characterize trabecular bone structure in a manner needed for radiation dosimetry models. High-field proton nuclear magnetic resonance (NMR) imaging is one such technology. NMR is an ideal modality for imaging trabecular bone due to the sharp contrast in proton density between the bone matrix and bone marrow regions. In this study, images of the trabecular regions within the bodies of a human thoracic vertebra have been obtained at a field strength of 14.1 T. These images were digitally processed to measure chord length distribution data through both the bone trabeculae and marrow cavities. These distributions, which were found to be qualitatively consistent with those measured by F. W. Spiers and colleagues at the University of Leeds using physical sectioning and automated light microscopy, yielded a mean trabecular thickness of 201 microm and a mean marrow cavity thickness of 998 microm. The NMR techniques developed here for vertebral imaging may be extended to other skeletal sites, allowing for improved site-specific skeletal dosimetry.