Amish P. Shah

Surface area overestimation within three-dimensional digital images and its consequence for skeletal dosimetry.

The most recent methods for trabecular bone dosimetry are based on Monte Carlo transport simulations within three-dimensional (3D) images of real human bone samples. Nuclear magnetic resonance and micro-computed tomography have been commonly used as imaging tools for studying trabecular microstructure. In order to evaluate the accuracy of these techniques for radiation dosimetry, a previous study was conducted that showed an overestimate in the absorbed fraction of energy for low-energy electrons emitted within the marrow space and irradiating the bone trabeculae. This problem was found to be related to an overestimate of the surface area of the true bone-marrow interface within the 3D digital images, and was identified as the surface-area effect. The goal of the present study is to better understand how this surface-area effect occurs in the case of single spheres representing individual marrow cavities within trabecular bone. First, a theoretical study was conducted which showed that voxelization of the spherical marrow cavity results in a 50% overestimation of the spherical surface area. Moreover, this overestimation cannot be reduced through a reduction in the voxel size (e.g., improved image resolution). Second, a series of single-sphere marrow cavity models was created with electron sources simulated within the sphere (marrow source) and outside the sphere (bone trabeculae source). The series of single-sphere models was then voxelized to represent 3D digital images of varying resolution. Transport calculations were made for both marrow and bone electron sources within these simulated images. The study showed that for low-energy electrons (<100 keV), the 50% overestimate of the bone-marrow interface surface area can lead to a 50% overestimate of the cross-absorbed fraction. It is concluded that while improved resolution will not reduce the surface area effects found within 3D image-based transport models, a tenfold improvement in current image resolution would compensate the associated errors in cross-region absorbed fractions for low-energy electron sources. Alternatively, other methods of defining the bone-marrow interface, such as with a polygonal isosurface, would provide improvements in dosimetry without the need for drastic reductions in image voxel size.

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.

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.

Accounting for beta-particle energy loss to cortical bone via paired-image radiation transport (PIRT)

Current methods of skeletal dose assessment in both medical physics (radionuclide therapy) and health physics (dose reconstruction and risk assessment) rely heavily on a single set of bone and marrow cavity chord-length distributions in which particle energy deposition is tracked within an infinite extent of trabecular spongiosa, with no allowance for particle escape to cortical bone. In the present study, we introduce a paired-image radiation transport (PIRT) model which provides a more realistic three-dimensional (3D) geometry for particle transport in the skeletal site at both microscopic and macroscopic levels of its histology. Ex vivo CT scans were acquired of the pelvis, cranial cap, and individual ribs excised from a 66-year male cadaver (BMI of 22.7 kg m(-2)). For the three skeletal sites, regions of trabecular spongiosa and cortical bone were identified and segmented. Physical sections of interior spongiosa were taken and subjected to microCT imaging. Voxels within the resulting microCT images were then segmented and labeled as regions of bone trabeculae, endosteum, active marrow, and inactive marrow through application of image processing algorithms. The PIRT methodology was then implemented within the EGSNRC radiation transport code whereby electrons of various initial energies are simultaneously tracked within both the ex vivo CT macroimage and the CT microimage of the skeletal site. At initial electron energies greater than 50-200 keV, a divergence in absorbed fractions to active marrow are noted between PIRT model simulations and those estimated under existing techniques of infinite spongiosa transport. Calculations of radionuclide S values under both methodologies imply that current chord-based models may overestimate the absorbed dose to active bone marrow in these skeletal sites by 0% to 27% for low-energy beta emitters (33P, 169Er, and 177Lu), by approximately 4% to 49% for intermediate-energy beta emitters (153Sm, 186Re, and 89Sr), and by approximately 14% to 76% for high-energy beta emitters (32p, 188Re, and 90Y). The PIRT methodology allows for detailed modeling of the 3D macrostructure of individual marrow-containing bones within the skeleton thus permitting improved estimates of absorbed fractions and radionuclide S values for intermediate-to-high energy beta emitters.

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.

Chord‐based versus voxel‐based methods of electron transport in the skeletal tissues

Anatomic models needed for internal dose assessment have traditionally been developed using mathematical surface equations to define organ boundaries, shapes, and their positions within the body. Many researchers, however, are now advocating the use of tomographic models created from segmented patient computed tomography (CT) or magnetic resonance (MR) scans. In the skeleton, however, the tissue structures of the bone trabeculae, marrow cavities, and endosteal layer are exceedingly small and of complex shape, and thus do not lend themselves easily to either stylistic representations or in-vivo CT imaging. Historically, the problem of modeling the skeletal tissues has been addressed through the development of chord-based methods of radiation particle transport, as given by studies at the University of Leeds (Leeds, U.K.) using a 44-year male subject. We have proposed an alternative approach to skeletal dosimetry in which excised sections of marrow-intact cadaver spongiosa are imaged directly via microCT scanning. The cadaver selected for initial investigation of this technique was a 66-year male subject of nominal body mass index (22.7 kg m(-2)). The objectives of the present study were to compare chord-based versus voxel-based methods of skeletal dosimetry using data from the UF 66-year male subject. Good agreement between chord-based and voxel-based transport was noted for marrow irradiation by either bone surface or bone volume sources up to 500-1000 keV (depending upon the skeletal site). In contrast, chord-based models of electron transport yielded consistently lower values of the self-absorbed fraction to marrow tissues than seen under voxel-based transport at energies above 100 keV, a feature directly attributed to the inability of chord-based models to account for nonlinear electron trajectories. Significant differences were also noted in the dosimetry of the endosteal layer (for all source tissues), with chord-based transport predicting a higher fraction of energy deposition than given by voxel-based transport (average factor of about 1.6). The study supports future use of voxel-based skeletal models which (1) permit nonlinear electron trajectories across the skeletal tissues, (2) do not rely on mathematical algorithms for treating the endosteal tissue layer, and (3) do not implicitly assume independence of marrow and bone trajectories as is the case for chord-based skeletal models.

A hyperboliod representation of the bone-marrow interface within 3D NMR images of trabecular bone: applications to skeletal dosimetry.

Recent advances in physical models of skeletal dosimetry utilize high-resolution NMR microscopy images of trabecular bone. These images are coupled to radiation transport codes to assess energy deposition within active bone marrow irradiated by bone- or marrow-incorporated radionuclides. Recent studies have demonstrated that the rectangular shape of image voxels is responsible for cross-region (bone-to-marrow) absorbed fraction errors of up to 50% for very low-energy electrons (<50 keV). In this study, a new hyperboloid adaptation of the marching cube (MC) image-visualization algorithm is implemented within 3D digital images of trabecular bone to better define the bone-marrow interface, and thus reduce voxel effects in the assessment of cross-region absorbed fractions. To test the method, a mathematical sample of trabecular bone was constructed, composed of a random distribution of spherical marrow cavities, and subsequently coupled to the EGSnrc radiation code to generate reference values for the energy deposition in marrow or bone. Next, digital images of the bone model were constructed over a range of simulated image resolutions, and coupled to EGSnrc using the hyperboloid MC (HMC) algorithm. For the radionuclides 33P, 117mSn, 131I and 153Sm, values of S(marrow<--bone) estimated using voxel models of trabecular bone were shown to have relative errors of 10%, 9%, <1% and <1% at a voxel size of 150 microm. At a voxel size of 60 microm, these errors were 6%, 5%, <1% and <1%, respectively. When the HMC model was applied during particle transport, the relative errors on S(marrow<--bone) for these same radionuclides were reduced to 7%, 6%, <1% and <1% at a voxel size of 150 microm, and to 2%, 2%, <1% and <1% at a voxel size of 60 microm. The technique was also applied to a real NMR image of human trabecular bone with a similar demonstration of reductions in dosimetry errors.