Volume effects on fatigue life of equine cortical bone

Materials, including bone, often fail due to loading in the presence of critical flaws. The relative amount, location, and interaction of these flaws within a stressed volume of material play a role in determining the failure properties of the structure. As materials are generally imperfect, larger volumes of material have higher probabilities of containing a flaw of critical size than do smaller volumes. Thus, larger volumes tend to fail at fewer cycles compared with smaller volumes when fatigue loaded to similar stress levels. A material is said to exhibit a volume effect if its failure properties are dependent on the specimen volume. Volume effects are well documented in brittle ceramics and composites and have been proposed for bone. We hypothesized that (1) smaller volumes of cortical bone have longer fatigue lives than similarly loaded larger volumes and (2) that compared with microstructural features, specimen volume was able to explain comparable amounts of variability in fatigue life. In this investigation, waisted rectangular specimens (n=18) with nominal cross-sections of 3×4 mm and gage lengths of 10.5, 21, or 42 mm, were isolated from the mid-diaphysis of the dorsal region of equine third metacarpal bones. These specimens were subjected to uniaxial load controlled fatigue tests, with an initial strain range of 4000 microstrain. The group having the smallest volume exhibited a trend of greater log fatigue life than the larger volume groups. Each volume group exhibited a significant positive correlation between the logarithm of fatigue life and the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log fatigue life was negatively correlated with log volume, supporting the hypothesis that smaller stressed volumes of cortical bone possess longer fatigue lives than similarly tested larger stressed volumes.     

植入了骨修复材料的小型猪腰椎椎体不脱钙病理组织切片制备方法

摘要 目的：建立植入了骨修复材料小型猪腰椎椎体骨组织标本的不脱钙病理组织切片制备方法。方法：将含骨修复材料的腰椎椎体骨组织标本进行分割暴露组织切面,梯度浓度乙醇脱水后经Technovit 7200 VLC光聚树脂浸润,经黄蓝光共同辐照进行光聚合包埋,借助硬组织病理切磨系统制备含骨修复材料不脱钙病理组织切片。结果：结果显示通过上述方法制备的病理组织切片,经苏木精-伊红（HE）染色及甲苯胺蓝染色后光学显微镜下观察能较好地显示骨的各种组织细胞结构,可清晰的观察到骨小梁的走向及连接情况。结论：研究建立了含骨修复材料骨组织标本病理组织切片制备方法,实现了含骨修复材料不脱钙骨组织病理切片的制备,经病理染色后实现了带植入物的组织学观察,为生物材料及医疗器械动物试验研究提供了新的病理检测手段及组织学评价途径。     

Identification of novel porcine endogenous betaretrovirus sequences in miniature swine

PCR amplification of genomic DNA from miniature swine peripheral blood lymphocytes, using primers corresponding to highly conserved regions of the polymerase (pol) gene, allowed the identification of two novel porcine endogenous retrovirus (PERV) sequences, PMSN-1 and PMSN-4. Phylogenetic analyses of the nucleotide sequences of PMSN-1 and PMSN-4 revealed them to be most closely related to betaretroviruses. The identification of PERVs belonging to the Betaretrovirus genus shows that endogenous retroviruses of this family are more broadly represented in mammalian species than previously appreciated. Both sequences contained inactivating mutations, implying that these particular loci are defective. However, Southern blot analysis showed additional copies of closely related proviruses in the miniature swine genome. Analyses of fetal and adult miniature swine tissues revealed a broad mRNA expression pattern of both PMSN-1 and PMSN-4. The most abundant expression was detected in whole bone marrow c-kit(+) (CD117(+)) progenitor bone marrow cells, fetal liver, salivary gland, and thymus. It appears unlikely that functional loci encoding these novel PERV sequences exist, but this remains to be established. The betaretrovirus sequences described in this report will allow such investigations to be actively pursued.     

Validation of composite finite elements efficiently simulating elasticity of trabecular bone

Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r_𝒸 ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.     

Functional cues in the development of osseous tooth support in the pig, Sus scrofa

Alveolar bone supports teeth during chewing through a ligamentous interface with tooth roots. Although tooth loads are presumed to direct the development and adaptation of these tissues, strain distribution in the alveolar bone at different stages of tooth eruption and periodontal development is unknown. This study investigates the biomechanical effects of tooth loading on developing alveolar bone as a tooth erupts into occlusion. Mandibular segments from miniature pigs, Sus scrofa, containing M₁ either erupting or in functional occlusion, were loaded in compression. Simultaneous recordings were made from rosette strain gages affixed to the lingual alveolar bone and the M₂ crypt. Overall, specimens with erupting M₁s were more deformable than specimens with occluding M₁s (mean stiffness of 246 vs. 944 MPa, respectively, p=0.004). The major difference in alveolar strain between the two stages was in orientation. The vertically applied compressive loads were more directly reflected in the alveolar bone strains of erupting M₁s, than those of occluding M₁s, presumably because of the mediation of a more mature periodontal ligament (PDL) in the latter. The PDL interface between occluding teeth and alveolar bone is likely to stiffen the system, allowing transmission of occlusal loads. Alveolar strains may provide a stimulus for bone growth in the alveolar process and crest.     

An Infiltration and Clearing Technic to Reveal the Vascular Pattern of Ethylenediamine-Treated Cortical Bone

The vascular canals of cortical bone are revealed by: (1) removing all organic tissue with ethylenediamine (ed), (2) infiltrating the Haversian and Volkmann canals with a pigment and (3) finally clearing the specimens in styrene. Buccal and lingual cortical plates of mandibles were freed of spongy bone and placed in a Soxhlet extractor. Extraction was carried out with a solution consisting of 4 volumes of ed and 1 volume of distilled water which was maintained at a temperature of 118°C for 24 hr. After extraction, the organic-free specimens were washed in water for 1 hr and dried. The dried bone was immersed in a 25% India ink suspension and placed in a vacuum chamber until bubbling ceased. The bones were then dried and the surface carbon was removed with a CO₂-driven stream of dolomite powder from an Airdent unit. Compressed air was used to remove the residual dolomite powder from the specimens. They were then immersed in styrene until clear. The specimens could be studied directly from the styrene, since the inorganic portion of the bone became transparent and carbon retained on the walls of the vascular channels within the calcified tissue was clearly visible. Plastic can be substituted for styrene for infiltrating the spaces within the specimen which were previously occupied by organic material. After infiltration and curing of the plastic, the embedded specimens can be decalcified with concentrated HCl. After decalcification, the voids created by the removal of the inorganic matrix can then be filled with plastic. Substituting plastic for areas previously occupied by both the organic and inorganic elements results in an easily visualized, carbon-black three-dimensional preparation of the vascular pattern of bone.     

A Versatile New Mineralized Bone Stain for Simultaneous Assessment of Tetracycline and Osteoid Seams

A versatile mineralized bone stain (MIBS) for demonstrating osteoid seams and tetracycline fluorescence simultaneously in thin or thick undecalcified sections has been developed. Bone specimens are fixed in 70% ethanol, but 10% buffered formalin is permissible. Depending upon one's preference, these specimens can be left unstained or be prestained before plastic embedding. Osteoid seams are stained green to jade green, or light to dark purple. Mineralized bone matrix is unstained or green. Osteoblast and osteoclast nuclei are light to dark purple, cytoplasm varies from slightly gray to pink. The identification of osteoid seams by this method agrees closely with identification by in vivo tetracycline uptake using the same section from the same biopsy. The method demonstrates halo volumes, an abnormal, lacunar, low density bone around viable osteocytes in purple. This phenomenon is commonly seen in vitamin D-resistant rickets, fluorosis, renal osteodystrophy, hyperparathyroidism, and is sometimes seen in fluoride treated osteoporotic patients. In osteomalacic bone, most osteoid seams are irregularly stained as indicated by the presence of unmineralized osteoid between mineralized lamellae. The method has been used effectively in staining new bone formation in hydroxyapatite implants and bone grafts. Old, unstained, plastic embedded undecalcified sections are stained as well as fresh sections after removal of the coverslip. This stain also promises to be valuable in the study of different metabolic bone diseases from the point of view of remodeling, histomorphometry, and pathology.     

Estimating Mass Properties of Dinosaurs Using Laser Imaging and 3D Computer Modelling

Body mass reconstructions of extinct vertebrates are most robust when complete to near-complete skeletons allow the reconstruction of either physical or digital models. Digital models are most efficient in terms of time and cost, and provide the facility to infinitely modify model properties non-destructively, such that sensitivity analyses can be conducted to quantify the effect of the many unknown parameters involved in reconstructions of extinct animals. In this study we use laser scanning (LiDAR) and computer modelling methods to create a range of 3D mass models of five specimens of non-avian dinosaur; two near-complete specimens of Tyrannosaurus rex, the most complete specimens of Acrocanthosaurus atokensis and Strutiomimum sedens, and a near-complete skeleton of a sub-adult Edmontosaurus annectens. LiDAR scanning allows a full mounted skeleton to be imaged resulting in a detailed 3D model in which each bone retains its spatial position and articulation. This provides a high resolution skeletal framework around which the body cavity and internal organs such as lungs and air sacs can be reconstructed. This has allowed calculation of body segment masses, centres of mass and moments or inertia for each animal. However, any soft tissue reconstruction of an extinct taxon inevitably represents a best estimate model with an unknown level of accuracy. We have therefore conducted an extensive sensitivity analysis in which the volumes of body segments and respiratory organs were varied in an attempt to constrain the likely maximum plausible range of mass parameters for each animal. Our results provide wide ranges in actual mass and inertial values, emphasizing the high level of uncertainty inevitable in such reconstructions. However, our sensitivity analysis consistently places the centre of mass well below and in front of hip joint in each animal, regardless of the chosen combination of body and respiratory structure volumes. These results emphasize that future biomechanical assessments of extinct taxa should be preceded by a detailed investigation of the plausible range of mass properties, in which sensitivity analyses are used to identify a suite of possible values to be tested as inputs in analytical models.     

Effect of mineral dissolution from bone specimens on the viscoelastic properties of cortical bone

Although physiological saline (0.15 M NaCl aqueous solution) has been used as a storage solution to prevent bone specimens from drying, there have been reports that Ca²⁺ ions dissolve from bone specimens during the storage in saline. In order to determine whether such storage has a marked effect on mechanical properties, the relaxation modulus of bovine cortical bone stored in physiological saline was compared with that stored in a buffer solution containing a sufficient amount of Ca²⁺ ions. After storage in saline, the modulus value of specimens was significantly reduced from that before storage. On the other hand, the modulus value of specimens soaked in the solution containing sufficient Ca²⁺ ions did not change after storage. The relaxation rate of a bone specimen stored in physiological saline was larger than that of a specimen stored in Ca²⁺-buffered saline solution and that of the control specimens. The results suggest that by the dissolution of Ca²⁺ ions from a bone specimen during storage in physiological saline, percolated paths of mineral phase and of reinforced matrix phase are disjoined, resulting in reduction in the elastic modulus and change in the viscoelastic properties of bone.     

Comparison of spectroscopy technologies for improved monitoring of cell culture processes in miniature bioreactors

Cell culture process development requires the screening of large numbers of cell lines and process conditions. The development of miniature bioreactor systems has increased the throughput of such studies; however, there are limitations with their use. One important constraint is the limited number of offline samples that can be taken compared to those taken for monitoring cultures in large‐scale bioreactors. The small volume of miniature bioreactor cultures (15 mL) is incompatible with the large sample volume (600 µL) required for bioanalysers routinely used. Spectroscopy technologies may be used to resolve this limitation. The purpose of this study was to compare the use of NIR, Raman, and 2D‐fluorescence to measure multiple analytes simultaneously in volumes suitable for daily monitoring of a miniature bioreactor system. A novel design‐of‐experiment approach is described that utilizes previously analyzed cell culture supernatant to assess metabolite concentrations under various conditions while providing optimal coverage of the desired design space. Multivariate data analysis techniques were used to develop predictive models. Model performance was compared to determine which technology is more suitable for this application. 2D‐fluorescence could more accurately measure ammonium concentration (RMSE_CV 0.031 g L^?1) than Raman and NIR. Raman spectroscopy, however, was more robust at measuring lactate and glucose concentrations (RMSE_CV 1.11 and 0.92 g L^?1, respectively) than the other two techniques. The findings suggest that Raman spectroscopy is more suited for this application than NIR and 2D‐fluorescence. The implementation of Raman spectroscopy increases at‐line measuring capabilities, enabling daily monitoring of key cell culture components within miniature bioreactor cultures. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:337–346, 2017     

The use of protein characteristics to assess the retrievability of ancient DNA from ancient bones

The ability to retrieve DNA from ancient specimens has been one of the greatest achievements of the past decade, and has opened a totally new field of research with applications in seemingly distant domains such as archeobotany, the molecular phylogeny of extinct genomes, human paleopathology and the genetic of ancient human populations. However, extraction of ancient DNA has often a very low rate of success, prompting researchers to develop screening methods for the selection of promising specimens. With this goal in mind, we studied the amino acid content of nine human bones of ancient origin. We demonstrate that a single HPLC chromatogram is indicative of the integrity of ancient bone proteins. Among five specimens containing amplifiable DNA, four exhibited a protein content similar to that of contemporary bone protein content. Three of the four specimens, from which we were unable to extract any amplifiable DNA, had an amino acid content strikingly different from that of contem-porary bone. A non-parametric statistical test, Kendall's tau, was used to show that protein content and PCR products, are probably correlated (at a 95% confidence level). In addition, the D/L Asp and D/L Glu racemization ratios obtained are indicative of the presence of ancient organic compounds. We propose that protein analysis should be systematically performed in studies where there are many samples in order to select the specimens that are most likely to contain retrievable ancient DNA.     

Accurate, rapid measurement of the fraction of unbound estradiol and progesterone in small volumes of undiluted serum at 37 degrees C by miniature steady-state gel filtration

A method is described for the accurate, rapid measurement of the unbound fractions of estradiol and of progesterone in small volumes of plasma or serum at 37 degrees C by a miniature method of steady-state gel filtration. There is minimal perturbation of the equilibrium between bound and free hormone and no derived kinetic parameters are required. The method has been used to measure the unbound fraction of progesterone in plasma from women during the second and third trimesters of pregnancy and of estradiol in sera of developing female rats.     

Interfacial Strength of Cement Lines in Human Cortical Bone

In human cortical bone, cement lines (or reversal lines) separate osteons from the interstitial bone tissue, which consists of remnants of primary lamellar bone or fragments of remodeled osteons. There have been experimental evidences of the cement line involvement in the failure process of bone such as fatigue and damage. However, there are almost no experimental data on interfacial properties of cement lines in human cortical bone. The objective of this study is to design and assemble a precision and computer controlled osteon pushout microtesting system, and to experimentally determine the interfacial strength of cement lines in human cortical bone by performing osteon pushout tests. Thirty specimens were prepared from humeral diaphyses of four human subjects. Twenty specimens were tested under the condition of a small hole in the supporting plate, in which the cement line debonding occurred. The cement line interfacial strength ranged from 5.38 MPa to 10.85 MPa with an average of 7.31±1.73 MPa. On the other hand, ten specimens were tested under the condition of a large hole in the supporting plate, in which the shear failure inside osteons was observed. The specimens tested under the condition of the large hole resulted in an average shear strength of 73.71±15.06 MPa, ranging from 45.97 MPa to 93.74 MPa. Therefore, our results suggest that the cement line interface between osteon and interstitial bone tissue is weaker than that between bone tissue lamellae.     

Angular orientation of trabecular bone in the femoral head and its relationship to hip joint loads in leaping primates

The elastic properties and mechanical behavior of trabecular bone are largely determined by its three-dimensional (3D) fabric structure. Recent work demonstrating a correlation between the primary mechanical and material axes in trabecular bone specimens suggests that fabric orientation may be used to infer directional components of the material strength and, by extension, the hypothetical loading regime. Here we quantify the principal orientation of trabecular bone in the femoral head and relate these principal fabric directions to loading patterns during various locomotor behaviors. The proximal femora of a diverse sample of prosimians were scanned using a high-resolution X-ray computed tomography scanner with resolution of better than 50 mum. Spherical volumes of interest were defined within the femoral heads and the 3D fabric anisotropy was calculated using the mean intercept length and star volume distribution methods. In addition to differences in bone volume and anisotropy, significant differences were found in the spatial orientation of the principal trabecular axes depending on locomotor behavior. The principal orientations for leapers (Galago, Tarsius, Avahi) are relatively tightly clustered (alpha(95) confidence limit: 8.2; angular variance s: 18.2 degrees ) and oriented in a superoanterior direction, while those of nonleapers are more variable across a range of directions (alpha(95): 16.8; s: 42.0 degrees ). The mean principal directions are significantly different for leaping vs. nonleaping taxa. These results further suggest a relationship between bone microstructure in the hip joint and locomotor behavior and indicate a similarity of loading across leapers despite differences in kinematics and phylogeny.     

The biomechanical analysis of bone strength: A method and its application to platycnemia

Traditional methods of bone analysis (both metric and topographic) are restricted to external characters. Spacial distribution of material is, however, equally critical to an understanding of a bone's function. Dynamic testing to determine whole bone strength can only be performed on fresh specimens. Methods for the calculation of both bending and torsional strength of other specimens (such as preserved or fossil bones) are developed in this paper. In order to illustrate the methods, the functional significance of tibial shaft cross sectional variation is investigated.     

Growth trajectories of some major ammonoid sub‐clades revealed by serial grinding tomography data

Molluscs such as ammonoids record their growth in their accretionary shells, making them ideal for the study of evolutionary changes in ontogeny through time. Standard methods usually focus on two‐dimensional data and do not quantify empirical changes in shell and chamber volumes through ontogeny, which can possibly be important to disentangle phylogeny, interspecific variation and palaeobiology of these extinct cephalopods. Tomographic and computational methods offer the opportunity to empirically study volumetric changes in shell and chamber volumes through ontogeny of major ammonoid sub‐clades in three dimensions (3‐D). Here, we document (1) the growth of chamber and septal volumes through ontogeny and (2) differences in ontogenetic changes between species from each of three major sub‐clades of Palaeozoic ammonoids throughout their early phylogeny. The data used are three‐dimensional reconstructions of specimens that have been subjected to grinding tomography. The following species were studied: the agoniatitid Fidelites clariondi and anarcestid Diallagites lenticulifer (Middle Devonian) and the Early Carboniferous goniatitid Goniatites multiliratus. Chamber and septum volumes were plotted against the septum number and the shell diameter (proxies for growth) in the three species; although differences are small, the trajectories are more similar among the most derived Diallagites and Goniatites compared with the more widely umbilicate Fidelites. Our comparisons show a good correlation between the 3‐D and the 2‐D measurements. In all three species, both volumes follow exponential trends with deviations in very early ontogeny (resolution artefacts) and near maturity (mature modifications in shell growth). Additionally, we analyse the intraspecific differences in the volume data between two specimens of Normannites (Middle Jurassic).     

三品系小型猪35个微卫星基因座的遗传学研究

利用35个微卫星基因座对中国三个品系的小型猪（贵州小型香猪、广西巴马小型猪、版纳小耳猪近交系）进行了遗传检测。计算出三个小型猪品系个体样本在35个微卫星基因座的纯合率,并对其进行t检验。计算出各品系的平均杂合度,多态信息含量（PIC）及品系间的遗传距离,并进行了系统聚类。结果表明三个品系的小型猪其基因纯合率均较高,其中版纳小耳猪近交系的基因纯合率最高;PIC和平均杂合度均较低;贵州小型香猪和广西巴马小型猪亲缘关系较近,并均与版纳小耳猪近交系的亲缘关系略远。 Abstract：The polymorphism of 35 microsatellites in the three miniature pig breeds in China(Guizhou miniature pig, Guangxi Bama miniature pig, Banna miniature pig inbred) was analysed. Rates of homozygote for 35 microsatellite loci in three miniature pig breeds were calculated,and t-test for them were performed. Mean heterozygosity and polymorphism information content(PIC) were calculated for all breeds, and genetic distances between these breeds were estimated. The dendrograms were obtained based on genetic distances. The results suggest that rates of homozygote in the three breeds are all high, and that is the highest in Banna miniature pig inbred. The results also suggest that polymorphism information content and mean heterozygosity in all the three breeds are low, and the genetic relationship between Guizhou miniature pig and Guangxi Bama miniature pig is closer than their relationship with Banna miniature pig inbred.     

Searching for DNA in museum specimens: a comparison of sources in a mammal species

The number of genetic studies that use preserved specimens as sources of DNA has been steadily increasing during the last few years. Therefore, selecting the sources that are more likely to provide a suitable amount of DNA of enough quality to be amplified and at the minimum cost to the original specimen is an important step for future research. We have compared different types of tissue (hides vs. bones) from museum specimens of Iberian lynx and multiple alternative sources within each type (skin, footpad, footpad powder, claw, diaphysis, maxilloturbinal bone, mastoid process and canine) for DNA yield and probability of amplification of both mitochondrial and nuclear targets. Our results show that bone samples yield more and better DNA than hides, particularly from sources from skull, such as mastoid process and canines. However, claws offer an amplification success as high as bone sources, which makes them the preferred DNA source when no skeletal pieces have been preserved. Most importantly, these recommended sources can be sampled incurring minimal damage to the specimens while amplifying at a high success rate for both mitochondrial and microsatellite markers.     

Biomechanical implications of degenerative joint disease in the apophyseal joints of human thoracic and lumbar vertebrae

An experimental technique for quantifying load-sharing in cadaveric spines is used to test the hypothesis that degenerative changes in human apophyseal joints are directly related to high levels of compressive load-bearing by these joints. About 36 cadaveric thoraco-lumbar motion segments aged 64-92 years were subjected to a compressive load of 1.5 kN. The distribution of compressive stress was measured in the intervertebral discs using a miniature pressure transducer, and stress measurements were summed over area to give the compressive force resisted by the disc. This was subtracted from the applied 1.5 kN to indicate compressive load-bearing by the apophyseal joints. The cartilage of each apophyseal joint surface was then graded for degree of degeneration. After maceration, each joint surface was scored for degenerative joint disease (DJD) affecting the bone. Results demonstrated that the apophyseal joints resisted 5-96% (mean 45%) of the applied compressive force. A significant positive correlation was demonstrated between age and cartilage degeneration, age and DJD bone score, apophyseal joint load-bearing and bone score, and cartilage score and load-bearing. The latter correlation was strongest for load-bearing above 50%. Ordinal regression showed that the variables describing bone DJD (marginal osteophytes, pitting, bony contour change, and eburnation) were significantly correlated with degree of cartilage degeneration. It is concluded that in elderly individuals apophyseal joint load-bearing above a threshold of 50% is associated with severe degenerative changes in cartilage and bone, and that markers of DJD observed palaeopathologically may be used as predictors of such loadingin life.     

Spectral analysis and connectivity of porous microstructures in bone

Cancellous bone is a porous composite of calcified tissue interspersed with soft marrow. Sea ice is also a porous composite, consisting of pure ice with brine, air, and salt inclusions. Interestingly, the microstructures of bone and sea ice exhibit notable similarities. In recent years, we have developed mathematical and experimental techniques for imaging and characterizing the brine microstructure of sea ice, such as its volume fraction and connectivity, as well as a range of theoretical approaches for studying fluid, thermal, and electromagnetic transport in sea ice. Here we explore the application of our sea ice techniques to investigate trabecular bone. For example, percolation theory that quantifies brine connectivity and its thermal evolution can also help assess the impact of osteoporosis on trabecular structure. Central to our approach is the spectral measure of a composite material, which contains detailed information about the mixture geometry, and can be used in powerful integral representations to compute the effective properties. The spectral measure is obtained from the eigenvalues and eigenvectors of a self-adjoint operator determined exclusively by the composite microgeometry. Here we compute the spectral measures for discretizations of images of healthy and osteoporotic bone. The measures are used to compute the effective electromagnetic properties of the bone specimens. These data are then inverted to reconstruct the porosity of the original specimens, with excellent agreement.