Fractal geometry and vertebral compression fractures

Mechanical Properties and Failure Mode of Proximal Screw Fixation Technique Using Locking Compression Plate for Proximal Interphalangeal Arthrodesis in Horses: An Ex Vivo Study

OBJECTIVE

 The aim of this study was to measure the mechanical properties and failure mode of an ex vivo model of proximal interphalangeal arthrodesis in horses with different methods of proximal screw fixation using a locking compression plate.

STUDY DESIGN

 Pastern joint arthrodesis with a 3-hole 4.5-mm narrow locking compression plate was performed on 20 forelimbs of equine cadavers, randomized into four groups based on the fixation method and type of proximal screw used: unicortical cortex, bicortical cortex, unicortical locking, bicortical locking. Single-cycle axial compression testing was conducted until failure. The frequency of implant plastic deformation was recorded. Bone failure analysis was performed through computed tomography examinations and fractal analysis.

RESULTS

 There were no differences in the analysed mechanical variables and fractal dimension among the groups. Transarticular screws showed a higher frequency of deformation (75%) regardless of the group. Both unicortical locking and bicortical locking groups deformed the plate more frequently.

CONCLUSION

 The type of screw used in the proximal hole of the locking compression plate and its method of anchoring in the proximal phalanx do not affect the mechanical properties of pastern arthrodesis in equine cadavers subjected to single-cycle axial compression tests until failure.

RANKL blockade for erosive hand osteoarthritis: a randomized placebo-controlled phase 2a trial

Erosive hand osteoarthritis (OA) is a prevalent and disabling disease with limited treatment options. Here we present the results of a monocentric, placebo-controlled, double-blind, randomized phase 2a clinical trial with denosumab, a receptor activator of nuclear factor-κB ligand inhibitor, evaluating the effects on structure modification in erosive hand OA. Patients were randomized to 48 weeks treatment with denosumab 60 mg every 3 months (n = 51, 41 females) or placebo (n = 49, 37 females). The primary (radiographic) endpoint was the change in the total Ghent University Scoring System (GUSS) at week 24, where positive changes correspond to remodeling and negative changes to erosive progression. Secondary endpoints were the change in the GUSS at week 48 and the number of new erosive joints at week 48 by the anatomical phase scoring system. Baseline mean GUSS (standard deviation) of target joints was 155.9 (69.3) in the denosumab group and 158.7 (46.8) in the placebo group. The primary endpoint was met with an estimated difference between groups of 8.9 (95% confidence interval (CI) 1.0 to 16.9; P = 0.024) at week 24. This effect was confirmed at week 48 (baseline adjusted GUSS (standard error of the mean) denosumab and placebo were 163.5 (2.9) and 149.2 (3.9), respectively; with an estimated difference between groups of 14.3 (95% CI 4.6 to 24.0; P = 0.003)). At patient level, more new erosive joints were developed in the placebo group compared with denosumab at week 48 (odds ratio 0.24 (95% CI 0.08 to 0.72); P = 0.009). More adverse events occurred in the placebo group (125 events in 44 patients (90%)) compared with the denosumab group (97 events in 41 patients (80%)). These results demonstrate that denosumab has structure modifying effects in erosive hand OA by inducing remodeling and preventing new erosive joints. EU Clinical Trials Register identifier 2015-003223-53 .

Interest of Bone Histomorphometry in Bone Pathophysiology Investigation: Foundation, Present, and Future

Despite the development of non-invasive methods, bone histomorphometry remains the only method to analyze bone at the tissue and cell levels. Quantitative analysis of transiliac bone sections requires strict methodologic conditions but since its foundation more 60 years ago, this methodology has progressed. Our purpose was to review the evolution of bone histomorphometry over the years and its contribution to the knowledge of bone tissue metabolism under normal and pathological conditions and the understanding of the action mechanisms of therapeutic drugs in humans. The two main applications of bone histomorphometry are the diagnosis of bone diseases and research. It is warranted for the diagnosis of mineralization defects as in osteomalacia, of other causes of osteoporosis as bone mastocytosis, or the classification of renal osteodystrophy. Bone biopsies are required in clinical trials to evaluate the safety and mechanism of action of new therapeutic agents and were applied to anti-osteoporotic agents such as bisphosphonates and denosumab, an anti-RANKL, which induces a marked reduction of the bone turnover with a consequent elongation of the mineralization period. In contrast, an increased bone turnover with an extension of the formation site is observed with teriparatide. Romosozumab, an anti-sclerostin, has a dual effect with an early increased formation and reduced resorption. Bone histomorphometric studies allow us to understand the mechanism of coupling between formation and resorption and to evaluate the respective role of bone modeling and remodeling. The adaptation of new image analysis techniques will help bone biopsy analysis in the future.

Erosive Hand Osteoarthritis: Incidence and Predictive Characteristics among Participants in the Osteoarthritis Initiative

OBJECTIVE

To evaluate age, sex, race, osteoarthritis severity, metabolic factors, and bone health as risk factors for incident erosive hand osteoarthritis (EHOA) at baseline and over 48-month period.

METHODS

This study was a longitudinal cohort design including participants from the Osteoarthritis Initiative with complete hand radiographs from baseline and 48-month visits who were eligible at baseline for incident EHOA. Individuals were classified as having EHOA if they had Kellgren-Lawrence (KL) grade≥2 in at least one interphalangeal joint on two different fingers and central erosion in at least one joint.

RESULTS

Of the 3365 individuals identified without prevalent EHOA at baseline, 86 (2.6%) developed EHOA during the 48-month period. Risk factors included being older [relative risk (RR) per standard deviation=0.76 (95% confidence interval 0.59, 0.98)], female [RR=1.73 (1.05, 2.85)], greater osteoarthritis severity (sum of KL grade 13.9 vs. 5.3, p<0.001) and less cortical width (1.38 vs 1.52 mm, p<0.001). After 48 months, people who developed EHOA were characterized by greater progressions of radiographic osteoarthritis (i.e., joint space narrowing, KL grade progression [RRs = 1.35 to 1.9] and loss of cortical thickness [RR = 1.23], adjusted for age, sex, race, body mass index, and baseline osteoarthritis severity (sum KL scores).

CONCLUSION

These findings present EHOA as a disorder of advanced age and female sex, strongly associated with severity of articular structural damage and its progression. Individuals who develop EHOA have thinner bones prior to EHOA development and as it progresses, suggesting EHOA as a disorder of skeletal frailty.

X-ray-based quantitative osteoporosis imaging at the spine

Osteoporosis is a metabolic bone disease with a high prevalence that affects the population worldwide, particularly the elderly. It is often due to fractures associated with bone fragility that the diagnosis of osteoporosis becomes clinically evident. However, early diagnosis would be necessary to initiate therapy and to prevent occurrence of further fractures, thus reducing morbidity and mortality. X-ray-based imaging plays a key role for fracture risk assessment and monitoring of osteoporosis. Whereas over decades dual-energy X-ray absorptiometry (DXA) has been the main method used and still reflects the reference standard, another modality reemerges with quantitative computed tomography (QCT) because of its three-dimensional advantages and the opportunistic exploitation of routine CT scans. Against this background, this article intends to review and evaluate recent advances in the field of X-ray-based quantitative imaging of osteoporosis at the spine. First, standard DXA with the recent addition of trabecular bone score (TBS) is presented. Secondly, standard QCT, dual-energy BMD quantification, and opportunistic BMD screening in non-dedicated CT exams are discussed. Lastly, finite element analysis and microstructural parameter analysis are reviewed.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Cortical Fractal Analysis and Collagen Crosslinks Content in Femoral Neck After Osteoporotic Fracture in Postmenopausal Women: Comparison with Osteoarthritis

The femoral neck (FN) has been previously characterized by thinner cortices in osteoporotic fracture (HF) when compared to hip osteoarthritis (HOA). The purposes of this study were to complete the previous investigations on FNs from HF and HOA by analyzing the complexity of the cortical structure and to approach the intrinsic properties of cortical bone by assessing the collagen crosslink contents. FN samples were obtained during arthroplasty in 35 postmenopausal women (HF; n = 17; mean age 79 ± 2 years; HOA; n = 18; mean age 66 ± 2 years). The cortical fractal dimension (Ct.FD) and lacunarity (Ct.Lac) derived from high-resolution peripheral quantitative tomography (isotropic voxel size: 82 μm) images of FN by using Ctan software and Fraclac running in ImageJ were analyzed. The collagen crosslinks content [pyridinoline, deoxypyridinoline, pentosidine (PEN)] were assessed in cortical bone. Ct.FD was significantly lower (p < 0.0001) in HF than HOA reflecting a decreased complexity and was correlated to the age and BMD. In two sub-groups, BMD- and age-matched, respectively, Ct.FD remained significantly lower in HF than HOA (p < 0.001). Ct.Lac was not different between HF and HOA. PEN content was two times higher in HF than HOA (p < 0.0001) independently of age. In conclusion, FN with HF was characterized by a less complex cortical texture and higher PEN content than HOA. In addition to the decreased bone mass and BMD previously reported, these modifications contribute to the lower bone quality in HF than HOA in postmenopausal women.

Cooperative strategy for a dynamic ensemble of classification models in clinical applications: the case of MRI vertebral compression fractures

PURPOSE

In clinical practice, the constructive consultation among experts improves the reliability of the diagnosis and leads to the definition of the treatment plan for the patient. Aggregation of the different opinions collected by many experts can be performed at the level of patient information, abnormality delineation, or final assessment.

METHODS

In this study, we present a novel cooperative strategy that exploits the dynamic contribution of the classification models composing the ensemble to make the final class assignment. As a proof of concept, we applied the proposed approach to the assessment of malignant infiltration in 103 vertebral compression fractures in magnetic resonance images.

RESULTS

The results obtained with repeated random subsampling and receiver operating characteristic analysis indicate that the cooperative system statistically improved ([Formula: see text]) the classification accuracy of individual modules as well as of that based on the manual segmentation of the fractures provided by the experts.

CONCLUSIONS

The performances have been also compared with those obtained with those of standard ensemble classification algorithms showing superior results.

Computational modelling of bone augmentation in the spine

Computational models are gaining importance not only for basic science, but also for the analysis of clinical interventions and to support clinicians prior to intervention. Vertebroplasty has been used to stabilise compression fractures in the spine for years, yet there are still diverging ideas on the ideal deposition location, volume, and augmentation material. In particular, little is known about the long-term effects of the intervention on the surrounding biological tissue. This review aims to investigate computational efforts made in the field of vertebroplasty, from the augmentation procedure to strength prediction and long-term in silico bone biology in augmented human vertebrae. While there is ample work on simulating the augmentation procedure and strength prediction, simulations predicting long-term effects are lacking. Recent developments in bone remodelling simulations have the potential to show adaptation to cement augmentation and, thus, close this gap.

Autologous implantation of BMP2-expressing dermal fibroblasts to improve bone mineral density and architecture in rabbit long bones

Cell-mediated gene therapy may treat bone fragility disorders. Dermal fibroblasts (DFb) may be an alternative cell source to stem cells for orthopedic gene therapy because of their rapid cell yield and excellent plasticity with bone morphogenetic protein-2 (BMP2) gene transduction. Autologous DFb or BMP2-expressing autologous DFb were administered in twelve rabbits by two delivery routes; a transcortical intra-medullar infusion into tibiae and delayed intra-osseous injection into femoral drill defects. Both delivery methods of DFb-BMP2 resulted in a successful cell engraftment, increased bone volume, bone mineral density, improved trabecular bone microarchitecture, greater bone defect filling, external callus formation, and trabecular surface area, compared to non-transduced DFb or no cells. Cell engraftment within trabecular bone and bone marrow tissue was most efficiently achieved by intra-osseous injection of DFb-BMP2. Our results suggested that BMP2-expressing autologous DFb have enhanced efficiency of engraftment in target bones resulting in a measurable biologic response by the bone of improved bone mineral density and bone microarchitecture. These results support that autologous implantation of DFb-BMP2 warrants further study on animal models of bone fragility disorders, such as osteogenesis imperfecta and osteoporosis to potentially enhance bone quality, particularly along with other gene modification of these diseases.

Differential Effects of Dabigatran and Warfarin on Bone Volume and Structure in Rats with Normal Renal Function

Background

Warfarin, a widely used anticoagulant, is a vitamin K antagonist impairing the activity of vitamin K-dependent Bone Gla Protein (BGP or Osteocalcin) and Matrix Gla Protein (MGP). Because dabigatran, a new anticoagulant, has no effect on vitamin K metabolism, the aim of this study was to compare the impact of warfarin and dabigatran administration on bone structure and vascular calcification.

Methods

Rats with normal renal function received for 6 weeks warfarin, dabigatran or placebo. Bone was evaluated immuno-histochemically and hystomorphometrically after double labelling with declomycin and calcein. Aorta and iliac arteries were examined histologically.

Results

Histomorphometric analysis of femur and vertebrae showed significantly decreased bone volume and increased trabecular separation in rats treated with warfarin. Vertebra analysis showed that the trabecular number was higher in dabigatran treated rats. Osteoblast activity and resorption parameters were similar among groups, except for maximum erosion depth, which was higher in warfarin treated rats, suggesting a higher osteoclastic activity. Therefore, warfarin treatment was also associated with higher bone formation rate/bone surface and activation frequency. Warfarin treatment may cause an increased bone turnover characterized by increased remodelling cycles, with stronger osteoclast activity compared to the other groups. There were no differences among experimental groups in calcium deposition either in aortic or iliac arteries.

Conclusions

These findings suggest for the first time that dabigatran has a better bone safety profile than warfarin, as warfarin treatment affects bone by reducing trabecular size and structure, increasing turnover and reducing mineralization. These differences could potentially result in a lower incidence of fractures in dabigatran treated patients.

Characterization of trabecular bone density with ultra-short echo-time MRI at 1.5, 3.0 and 7.0 T--comparison with micro-computed tomography

The goal of this study was to test the potential of ultra-short echo-time (UTE) MRI at 1.5, 3.0 and 7.0 T for depiction of trabecular bone structure (of the wrist bones), to evaluate whether T2* relaxation times of bone water and parametric maps of T2* of trabecular bone could be obtained at all three field strengths, and to compare the T2* relaxation times with structural parameters obtained from micro-computed tomography (micro-CT) as a reference standard. Ex vivo carpal bones of six wrists were excised en bloc and underwent MRI at 1.5, 3.0 and 7.0 T in a whole-body MR imager using the head coil. A three-dimensional radial fat-suppressed UTE sequence was applied with subsequent acquisitions, with six different echo times TE of 150, 300, 600, 1200, 3500 and 7000 µs. The T2* relaxation time and pixel-wise computed T2* parametric maps were compared with a micro-computed-tomography reference standard providing trabecular bone structural parameters including porosity (defined as the bone-free fraction within a region of interest), trabecular thickness, trabecular separation, trabecular number and fractal dimension (Dk). T2* relaxation curves and parametric maps could be computed from datasets acquired at all field strengths. Mean T2* relaxation times of trabecular bone were 4580 ± 1040 µs at 1.5 T, 2420 ± 560 µs at 3.0 T and 1220 ± 300 µs at 7.0 T, when averaged over all carpal bones. A positive correlation of T2* with trabecular bone porosity and trabecular separation, and a negative correlation of T2* relaxation time with trabecular thickness, trabecular number and fractal dimension, was detected (p < 0.01 for all field strengths and micro-CT parameters). We conclude that UTE MRI may be useful to characterize the structure of trabecular bone, comparable to micro-CT.

Trabecular bone score: a noninvasive analytical method based upon the DXA image

The trabecular bone score (TBS) is a gray-level textural metric that can be extracted from the two-dimensional lumbar spine dual-energy X-ray absorptiometry (DXA) image. TBS is related to bone microarchitecture and provides skeletal information that is not captured from the standard bone mineral density (BMD) measurement. Based on experimental variograms of the projected DXA image, TBS has the potential to discern differences between DXA scans that show similar BMD measurements. An elevated TBS value correlates with better skeletal microstructure; a low TBS value correlates with weaker skeletal microstructure. Lumbar spine TBS has been evaluated in cross-sectional and longitudinal studies. The following conclusions are based upon publications reviewed in this article: 1) TBS gives lower values in postmenopausal women and in men with previous fragility fractures than their nonfractured counterparts; 2) TBS is complementary to data available by lumbar spine DXA measurements; 3) TBS results are lower in women who have sustained a fragility fracture but in whom DXA does not indicate osteoporosis or even osteopenia; 4) TBS predicts fracture risk as well as lumbar spine BMD measurements in postmenopausal women; 5) efficacious therapies for osteoporosis differ in the extent to which they influence the TBS; 6) TBS is associated with fracture risk in individuals with conditions related to reduced bone mass or bone quality. Based on these data, lumbar spine TBS holds promise as an emerging technology that could well become a valuable clinical tool in the diagnosis of osteoporosis and in fracture risk assessment.

Bone sparing effect of a novel phytoestrogen diarylheptanoid from Curcuma comosa Roxb. in ovariectomized rats

Phytoestrogens have been implicated in the prevention of bone loss in postmenopausal osteoporosis. Recently, an active phytoestrogen from Curcuma comosa Roxb, diarylheptanoid (DPHD), (3R)-1,7-diphenyl-(4E,6E)-4,6-heptadien-3-ol, was found to strongly promote human osteoblast function in vitro. In the present study, we demonstrated the protective effect of DPHD on ovariectomy-induced bone loss (OVX) in adult female Sprague-Dawley rats with 17β-estradiol (E₂, 10 µg/kg Bw) as a positive control. Treatment of OVX animals with DPHD at 25, 50, and 100 mg/kg Bw for 12 weeks markedly increased bone mineral density (BMD) of tibial metaphysis as measured by peripheral Quantitative Computed Tomography (pQCT). Histomorphometric analysis of bone structure indicated that DPHD treatment retarded the ovariectomy-induced deterioration of bone microstructure. Ovariectomy resulted in a marked decrease in trabecular bone volume, number and thickness and these changes were inhibited by DPHD treatment, similar to that seen with E₂. Moreover, DPHD decreased markers of bone turnover, including osteocalcin and tartrate resistant acid phosphatase (TRAP) activity. These results suggest that DPHD has a bone sparing effect in ovariectomy-induced trabecular bone loss and prevents deterioration of bone microarchitecture by suppressing the rate of bone turnover. Therefore, DPHD appears to be a promising candidate for preserving bone mass and structure in the estrogen deficient women with a potential role in reducing postmenopausal osteoporosis.

Differential characteristics of bone quality and bone turnover biochemical markers in patients with hip fragility fractures and hip osteoarthritis: results of a clinical pilot study

BACKGROUND AND AIMS

Bone density and quality alterations worsen the ability of osteoporotic bone to support prosthetic implants. The aim of our study was to evaluate potential differences in bone quality and bone turnover markers in aged individuals undergoing surgery for hip fragility fracture or hip osteoarthritis.

METHODS

Eighteen subjects with hip fragility fractures (Hip Fracture Group), 35 subjects with osteoarthritis of the hip (Hip Osteoarthritis Group) and 19 subjects with normal femoral bone mineral density (Control Group) were evaluated. Serum and urinary bone markers were assayed preoperatively in all surgical patients, and within 48 hours after fracture in the Hip Fracture, Osteoarthritis and Control groups. Histomorphometric analysis was performed on surgical samples.

RESULTS

A significant alteration in calcium and PTH serum levels with hyperparathyroidism was observed in the Hip Fracture Group compared with Hip Osteoarthritis and Control Groups. C-Terminal telopeptides of type I-collagen (CTx) and tartrate resistant-acid phosphatase (TRAP), markers of bone resorption, were increased in the Hip Fracture Group compared with both Osteoarthritis and Control Groups (CTx: p<0.0007 and p<0.0039 respectively; TRAP: p<0.002 and p<0.0007). All subjects were vitamin D3-deficient, but no differences were found among the different groups. In addition, histomorphometric data showed better maintained connectivity in the Osteoarthritis Group compared with the Hip Fracture Group (p<0.0001).

CONCLUSIONS

Our data show significant differences in bone turnover markers in patients undergoing hip prosthesis for fragility fractures, compared with patients operated for hip osteoarthritis.

Texture analysis, bone mineral density, and cortical thickness of the proximal femur: fracture risk prediction

OBJECTIVE

The objectives of this study were to perform a clinical study analyzing bone quality in multidetector computed tomographic images of the femur using bone mineral density (BMD), cortical thickness, and texture algorithms in differentiating osteoporotic fracture and control subjects; to differentiate fracture types.

METHODS

Femoral head, trochanteric, intertrochanteric, and upper and lower neck were segmented (fracture, n = 30; control, n = 10). Cortical thickness, BMD, and texture analysis were obtained using co-occurrence matrices, Minkowski dimension, and functional and scaling index method.

RESULTS

Bone mineral density and cortical thickness performed best in the neck region, and texture measures performed best in the trochanter. Only cortical thickness and texture measures differentiated femoral neck and intertrochanteric fractures.

CONCLUSIONS

This study demonstrates that differentiation of osteoporotic fracture subjects and controls is achieved with texture measures, cortical thickness, and BMD; however, performance is region specific.

Trabecular morphometry by fractal signature analysis is a novel marker of osteoarthritis progression

OBJECTIVE

To evaluate the effectiveness of using subchondral bone texture observed on a radiograph taken at baseline to predict progression of knee osteoarthritis (OA) over a 3-year period.

METHODS

A total of 138 participants in the Prediction of Osteoarthritis Progression study were evaluated at baseline and after 3 years. Fractal signature analysis (FSA) of the medial subchondral tibial plateau was performed on fixed flexion radiographs of 248 nonreplaced knees, using a commercially available software tool. OA progression was defined as a change in joint space narrowing (JSN) or osteophyte formation of 1 grade according to a standardized knee atlas. Statistical analysis of fractal signatures was performed using a new model based on correlating the overall shape of a fractal dimension curve with radius.

RESULTS

Fractal signature of the medial tibial plateau at baseline was predictive of medial knee JSN progression (area under the curve [AUC] 0.75, of a receiver operating characteristic curve) but was not predictive of osteophyte formation or progression of JSN in the lateral compartment. Traditional covariates (age, sex, body mass index, knee pain), general bone mineral content, and joint space width at baseline were no more effective than random variables for predicting OA progression (AUC 0.52-0.58). The predictive model with maximum effectiveness combined fractal signature at baseline, knee alignment, traditional covariates, and bone mineral content (AUC 0.79).

CONCLUSION

We identified a prognostic marker of OA that is readily extracted from a plain radiograph using FSA. Although the method needs to be validated in a second cohort, our results indicate that the global shape approach to analyzing these data is a potentially efficient means of identifying individuals at risk of knee OA progression.

Trabecular bone microarchitecture in mild primary hyperparathyroidism

Primary hyperparathyroidism (PHPT) is a common endocrine disease. High levels of PTH cause demineralization of bone and increased risk of fracture. On the other hand, the effect of PHPT on bone structure is more ambiguous. The aim of this study was to evaluate the effect of PHPT on cancellous bone volume, structure, and microarchitecture. Thirteen transiliac biopsy specimens taken in untreated post-menopausal women aged 65+/-5 yr with primary hyperparathyroidism were compared with 13 biopsies taken in normal women aged 66+/-6 yr. None of the patients presented any other disorder affecting bone metabolism. In these samples we evaluated the direct and indirect histomorphometric parameters of bone microarchitecture using an image analysis system consisting of an epifluorescent microscope (Leica DMR) connected to an analogic 3 CCD camera (Sony DXC 390P) and a computer equipped with specific software for histomorphometric analyses. No significant differences between PHPT patients and controls in cancellous bone volume, trabecular thickness, and number were found. Two-dimensional parameters showed a preserved microarchitecture in PHPT patients. On the other hand, indirect parameters of microarchitecture [Marrow Star Volume (MSV) and Trabecular Bone Pattern Factor (TBPf)] showed a significant compromising of microarchitecture in these patients. PHPT patients have similar structural parameters to normal subjects. Concerning microarchitecture, indirect approach by MSV and TBPf shows a significant compromising of connectivity. These results can explain trabecular fragility observed in clinical studies on PHPT.

Assessment and classification of mechanical strength components of human femur trabecular bone using texture analysis and neural network

In this work the mechanical strength components of human femur trabecular bone are analyzed and classified using planar radiographic images and neural network. The mechanical strength regions such as Primary Compressive, Primary Tensile, Secondary Tensile and Ward Triangle in femur trabecular bone images (N = 100) are delineated by semi-automatic image processing procedure. First and higher order texture parameters and parameters such as apparent mineralization and total area associated with the strength regions are derived for normal and abnormal images. The statistically derived significant parameters corresponding to the primary strength regions are fed to the neural network for training and validation. The classifications are carried out using feed forward network that is trained with standard back propagation algorithm. Results demonstrate that the apparent mineralization of normal samples is always high as (71%) compared to abnormal samples (64%). Entropy shows a high value (7.3) for normal samples and variation between the mean intensity and apparent mineralization for the primary strength zone is statistically significant (p < 0.0005). The classified outputs are validated by sensitivity and specificity measurements and are found to be 66.66% and 80% respectively. Further it appears that it is possible to differentiate normal and abnormal samples from the conventional radiographic images. As trabecular architecture in the human femur is an important factor contributing to bone strength, the procedure adopted here could be a useful supplement to the clinical observations for bone loss and fracture risk.

Risedronate prevents the loss of microarchitecture in glucocorticoid-induced osteoporosis in rats

Osteoporosis is a severe complication of glucocorticoid treatment. Bisphosphonates are a powerful therapeutic option to prevent osteoporotic fractures. The aims of this study were: a) to determine bone alterations induced by therapy with glucocorticoids (GC); b) to establish the efficacy of risedronate (Ris) in the prevention of these effects. We studied 40 female Sprague-Dawley rats randomly divided into 4 groups of treatment, administered 3 times a week sc: 1.

CONTROL

vehicle of methylprednisolone (GC) + vehicle of Ris; 2. Ris: Ris 5 mug/kg body weight vehicle of GC; 3. GC: GC 7 mg/kg + vehicle of Ris; 4. GC+Ris: GC 7 mg/kg, Ris 5 microg/kg. Animals were treated for 30 days and then were sacrificed. Densitometry was performed at baseline and at the end of the treatment. Right tibiae were removed for histomorphometric analyses. The GC group showed a 7% decrease in bone density vs controls (p<0.05), while the GC+Ris group was associated with a 3.5% increase in bone density vs controls (p<0.05). In the GC group, histomorphometric evaluations showed reduced bone volume (BV/TV) and thinning of trabeculae (Tb.Th) vs controls (BV/TV: 31+/-1 vs 35+/-1%, p<0.05; Tb.Th: 43+/-2 vs 50+/-3 microm, p<0.01; Ac.f: 1.8+/-0.2 vs 1.6+/-0.3 N/yr). The GC+Ris group had increased BV/TV and Tb.Th, and reduced Ac.f vs the GC group. Ris also maintained trabecular microarchitecture. At the histological level, glucocorticoid-induced osteoporosis was characterized by decreased bone volume, reduced osteoblastic activity, and deterioration of microarchitecture. Ris counteracted these effects both by prolonging osteoblast activity, and by maintaining bone microarchitecture.

Fractal analysis of contours of breast masses in mammograms

Fractal analysis has been shown to be useful in image processing for characterizing shape and gray-scale complexity. Breast masses present shape and gray-scale characteristics that vary between benign masses and malignant tumors in mammograms. Limited studies have been conducted on the application of fractal analysis specifically for classifying breast masses based on shape. The fractal dimension of the contour of a mass may be computed either directly from the 2-dimensional (2D) contour or from a 1-dimensional (1D) signature derived from the contour. We present a study of four methods to compute the fractal dimension of the contours of breast masses, including the ruler method and the box counting method applied to 1D and 2D representations of the contours. The methods were applied to a data set of 111 contours of breast masses. Receiver operating characteristics (ROC) analysis was performed to assess and compare the performance of fractal dimension and four previously developed shape factors in the classification of breast masses as benign or malignant. Fractal dimension was observed to complement the other shape factors, in particular fractional concavity, in the representation of the complexity of the contours. The combination of fractal dimension with fractional concavity yielded the highest area (A ( z )) under the ROC curve of 0.93; the two measures, on their own, resulted in A ( z ) values of 0.89 and 0.88, respectively.

Preservation of thoracic spine microarchitecture by alendronate: comparison of histology and microCT

The effect of bisphosphonates on trabecular microarchitecture may contribute to the reduced risk of vertebral fracture with treatment independent of the bone volume. Trabecular structure was examined at the twelfth thoracic vertebra after 2 years of treatment of two groups of ovariectomized baboons on high and low doses of alendronate, compared with ovariectomized and non-ovariectomized controls. Standard 2D histological measurements showed that alendronate treatment of ovariectomized animals resulted in significantly higher total trabecular length and a lower marrow star volume in comparison with ovariectomized controls indicating preservation of connectivity. Similarly when the vertebrae were examined using a novel thick slice technique that combines 2D and 3D information, ovariectomy produced a significantly higher number of "real" trabecular termini in comparison with normal. When ovariectomized animals were treated with increasing doses of alendronate, fewer "real" termini were seen. MicroCT analysis (2D and 3D) correlated well with the histological measurements, although more variability and less discrimination between groups was seen, with no statistically significant differences with alendronate treatment. Reduced vertebral fracture risk with alendronate may be due to a combination of factors including the increased bone volume, reduced turnover and greater mineralization reported by others. Added to this is now suggested the preservation of several aspects of vertebral cancellous architecture, with microscopy the most sensitive method of analysis.

Bone microarchitecture evaluated by histomorphometry

The increasing use of densitometric devices for assessing bone fragility has progressively strengthened the assumption that mass is the most important property determining bone mechanical competence. Nevertheless, structure and microarchitecture are relevant aspects of bone strength. The study of microarchitecture is based on the measure of width, number, and separation of trabeculae as well as on their spatial organization. There are several methods to assess bone architecture, particularly at the trabecular level. In particular, histomorphometry, based on the use of optical microscopy and on the principles of quantitative histology and stereology, evaluates microarchitecture two-dimensionally, even if these measures appear well correlated to the three-dimensional structure and properties of bone. In addition, new computerized methods allow the acquisition of more sophisticated measurements by means of a digitizer have been introduced to integrate the use of the microscope. These methods supply information on trabecular width as well as on its distribution and on the organization of the trabeculae in the marrow space. Microarchitecture seems to be a determinant of bone fragility independent of bone density and it is important for understanding the mechanisms of bone fragility as well as the action of the drugs used to prevent osteoporotic fractures. Several in vivo studies (on animals and humans) can provide an additional interpretation for the anti-fracture effect of such drugs. For instance, bisphosphonates and parathyroid hormone seem to preserve or even improve microarchitecture. The challenge for the future will be to evaluate bone quality in vivo with the same or better resolution and accuracy than the invasive methods used today.

Histomorphometric analysis of glucocorticoid-induced osteoporosis

Bone histomorphometry or quantitative histology consists of counting or measuring tissue components: cells, extracellular constituents and microarchitecture. Bone histomorphometry is the only method that allows the measurement of mineralization rate and the study of bone formation at three levels: cell, remodeling unit and tissue levels. It is a useful tool to explain the pathogenesis and cellular mechanisms of different metabolic bone diseases such as glucocorticoid-induced osteoporosis (GIO). Glucocorticoids (GC) affect calcium and bone metabolism at every level, but the main effect is the osteoblastic dysfunction. Concerning the bone formation, some histomorphometric studies have shown a depressed osteoblastic activity at a cell, bone remodeling unit, and tissue levels. In addition, there is evidence of a shortening of the period in which the osteoblasts work actively forming the bone matrix. This latter effect seems to occur after high cumulative doses of GC. With regard to the resorption, the results are still debated, but histomorphometric parameters seem to be increased in the majority of studies, at least in the first period of the GC treatment. From a structural point of view, GC seem to induce a thinning of the trabeculae without their perforation, which occurs only after high cumulative doses. Anti-resorptive treatments, such as bisphosphonates, are able to counteract the negative effects of GC on bone. In particular, along with their active working period, they prolong the lifespan of osteoblasts and osteocytes. In addition, the anti-resorptive treatments seem to extend the time for secondary mineralization through a reduction of the Activation Frequency. The latter is an intriguing mechanism of bisphosphonates in GIO that needs further ad hoc investigations.

Comparison insight bone measurements by histomorphometry and microCT

Morphometric analysis of 70 bone biopsies was done in parallel by microCT and histomorphometry. microCT provided higher results for trabecular thickness and separation because of the 3D shape of these anatomical objects.

INTRODUCTION

Bone histomorphometry is used to explore the various metabolic bone diseases. The technique is done on microscopic 2D sections, and several methods have been proposed to extrapolate 2D measurements to the 3D dimension. X-ray microCT is a recently developed imaging tool to appreciate 3D architecture. Recently the use of 2D histomorphometric measurements have been shown to provide discordant results compared with 3D values obtained directly.

MATERIAL AND METHODS

Seventy human bone biopsies were removed from patients presenting with metabolic bone diseases. Complete bone biopsies were examined by microCT. Bone volume (BV/TV), Tb.Th, and Tb.Sp were measured on the 3D models. Tb.Th and Tb.Sp were measured by a method based on the sphere algorithm. In addition, six images were resliced and transferred to an image analyzer: bone volume and trabecular characteristics were measured after thresholding of the images. Bone cores were embedded undecalcified; histological sections were prepared and measured by routine histomorphometric methods providing another set of values for bone volume and trabecular characteristics. Comparison between the different methods was done by using regression analysis, Bland-Altman, Passing-Bablock, and Mountain plots.

RESULTS

Correlations between all parameters were highly significant, but microCT overestimated bone volume. The osteoid volume had no influence in this series. Overestimation may have been caused by a double threshold used in microCT, giving trabecular boundaries less well defined than on histological sections. Correlations between Tb.Th and Tb.Sp values obtained by 3D or 2D measurements were lower, and 3D analysis always overestimated thickness by approximately 50%. These increases could be attributed to the 3D shape of the object because the number of nodes and the size of the marrow cavities were correlated with 3D values.

CONCLUSION

In clinical practice, microCT seems to be an interesting method providing reliable morphometric results in less time than conventional histomorphometry. The correlation coefficient is not sufficient to study the agreement between techniques in histomorphometry. The architectural descriptors are influenced by the algorithms used in 3D.

Relationship between compressive properties of human os calcis cancellous bone and microarchitecture assessed from 2D and 3D synchrotron microtomography

The aim of this study was to determine the contribution of 2D and 3D microarchitectural characteristics in the assessment of the mechanical strength of os calcis cancellous bone. A sample of cancellous bone was removed in a medio-lateral direction from the posterior body of calcaneus, taken at autopsy in 17 subjects aged 61-91 years. The sample was first used for the assessment of morphological parameters from 2D morphometry and 3D synchrotron microtomography (microCT) (spatial resolution=10 microm). The 2D morphometry was obtained from three slices extracted from the 3D microCT images. Very good concordance was shown between 3D microCT slices and the corresponding physical histologic slices. In 2D, the standard histomorphometric parameters, fractal dimension, mean intercept length, and connectivity were computed. In 3D, histomorphometric parameters were computed using both the 3D mean intercept length method and model-independent techniques. The 3D fractal dimension and the 3D connectivity, assessed by Euler density, were also evaluated. The cubic samples were subjected to elastic compressive tests in three orthogonal directions (X, Y, Z) close to the main natural trabecular network directions. A test was performed until collapse of trabecular network in the main direction (Z). The mechanical properties were significantly correlated to most morphological parameters resulting from 2D and 3D analysis. In 2D, the correlation between the mechanical strength and bone volume/tissue volume was not significantly improved by adding structural parameters or connectivity parameter (nodes number/tissue volume). In 3D, one architectural parameter (the trabecular thickness, Tb.Th) permitted to improve the estimation of the compressive strength from the bone volume/tissue volume alone. However, this improvement was minor since the correlation with the BV/TV alone was high (r=0.96). In conclusion, which is in agreement with the statistic's rules, we found, in this study, that the determination of the os calcis bone compressive strength using the 3D bone volume fraction cannot be improved by adding 3D architectural parameters.

Bone microarchitecture as an important determinant of bone strength

Structure and microarchitecture are determinant aspects of bone strength and essential elements for the assessment of bone mechanical properties. The main structural determinants of bone mechanical strength include width and porosity in the cortical bone; shape, width, connectivity, and anisotropy in the trabecular bone. There are several methods to assess bone architecture, particularly at the trabecular level. Two different approaches can be identified. The first is based on the use of optical microscopy and on the principles of quantitative histology, which evaluate microarchitecture two-dimensionally. The second applies the most modern diagnostic techniques, employing computed tomography and magnetic resonance to obtain and analyze three-dimensional images. From a clinical point of view, microarchitecture is an interesting aspect to study and define specific patterns, such as glucocorticoid-induced osteoporosis, or to evaluate bone alterations in transplanted patients. Microarchitecture seems to be a determinant of bone fragility independent of bone density. Moreover, bone microarchitecture seems to be important to understand the mechanisms of bone fragility as well as the action of the drugs used to prevent osteoporotic fractures. Several in vivo studies (on animals and humans) showed important findings on the effects of different treatments on microarchitecture. Bisphosphonates and parathyroid hormone seemed to preserve or even improve microarchitecture. These observations can provide an additional interpretation for the anti-fracture effect of drugs from a structural viewpoint. The challenge for the future will be to evaluate bone quality in vivo with the same or better resolution and accuracy than the invasive methods in use today.

Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity

Trabecular bone has been reported as having two-dimensional (2-D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared three algorithms on the same series of bone biopsies, to obtain the Kolmogorov, Minkowski-Bouligand, and mass-radius fractal dimensions. The relationships with histomorphometric descriptors of the 2-D trabecular architecture were investigated. Bone biopsies were obtained from 148 osteoporotic male patients. Bone volume (BV/TV), trabecular characteristics (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces and trabeculae), inter-connectivity index, and Euler-Poincaré number were computed. The box-counting method was used to obtain the Kolmogorov dimension (D(k)), the dilatation method for the Minkowski-Bouligand dimension (D(MB)), and the sandbox for the mass-radius dimension (D(MR)) and lacunarity (L). Logarithmic relationships were observed between BV/TV and the fractal dimensions. The best correlation was obtained with D(MR) and the lowest with D(MB). Lacunarity was correlated with descriptors of the marrow cavities (ICI, star volume, Tb.Sp). Linear relationships were observed among the three fractal techniques which appeared highly correlated. A cluster analysis of all histomorphometric parameters provided a tree with three groups of descriptors: for trabeculae (Tb.Th, strut); for marrow cavities (Euler, ICI, Tb.Sp, star volume, L); and for the complexity of the network (Tb.N and the three D's). A sole fractal dimension cannot be used instead of the classic 2-D descriptors of architecture; D rather reflects the complexity of branching trabeculae. Computation time is also an important determinant when choosing one of these methods.

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

Fractal analyses of osseous healing using tuned aperture computed tomography images

The aim of this study was to evaluate osseous healing in mandibular defects using fractal analyses on conventional radiographs and tuned aperture computed tomography (TACT; OrthoTACT, Instrumentarium Imaging, Helsinki, Finland) images. Eighty test sites on the inferior margins of rabbit mandibles were subject to lesion induction and treated with one of the following: no treatment (controls); osteoblasts only; polymer matrix only; or osteoblast-polymer matrix (OPM) combination. Images were acquired using conventional radiography and TACT, including unprocessed TACT (TACT-U) and iteratively restored TACT (TACT-IR). Healing was followed up over time and images acquired at 3, 6, 9, and 12 weeks post-surgery. Fractal dimension (FD) was computed within regions of interest in the defects using the TACT workbench. Results were analyzed for effects produced by imaging modality, treatment modality, time after surgery and lesion location. Histomorphometric data were available to assess ground truth. Significant differences (p < 0.0001) were noted based on imaging modality with TACT-IR recording the highest mean fractal dimension (MFD), followed by TACT-U and conventional images, in that order. Sites treated with OPM recorded the highest MFDs among all treatment modalities (p < 0.0001). The highest MFD based on time was recorded at 3 weeks and differed significantly with 12 weeks (p < 0.035). Correlation of FD with results of histomorphometric data was high (r = 0.79; p < 0.001). The FD computed on TACT-IR showed the highest correlation with histomorphometric data, thus establishing the fact TACT is a more efficient and accurate imaging modality for quantification of osseous changes within healing bony defects.

Effect of vitamin K2 on three-dimensional trabecular microarchitecture in ovariectomized rats

Menatetrenone, a vitamin K2 with four isoprene units, has been reported to improve osteoporotic bone loss. The purpose of this investigation was to clarify the effect of menatetrenone on the three-dimensional (3D) trabecular microarchitecture in ovariectomized (OVX) rats by using microcomputed tomography (MCT). Forty-two 13-week-old female rats were used and divided into four groups: the OVX (OVX + MK-4) group treated with menatetrenone, the (OVX untreated) group, the sham-operated (Sham + MK-4) group treated with menatetrenone, and the sham-operated group not treated with menatetrenone (Sham untreated) group. OVX rats were fed a calcium-deficient diet. Menatetrenone treatment was begun just after the ovariectomy, and the mean menatetrenone oral intake over the 8-week period was adjusted to 30 mg/kg BW per day. The proximal metaphyseal region of the right tibia was evaluated by dual X-ray absorptiometry (DXA) and MCT. A parametric analysis of the reconstructed trabecular volume was carried out using bone volume fractions, the fractal dimension calculated by the 3D box-counting method, and the connectivity density as determined by topological analysis. Menatetrenone significantly increased the trabecular bone volume, fractal dimension, and connectivity in the OVX + MK-4 group compared with the OVX-untreated group (p < 0.01). Our results suggest that an 8-week administration of menatetrenone protects against the loss of trabecular bone volume and its connectivity when treatment is begun just after the ovariectomy. Despite this apparent protection, it remains unknown whether it is possible to reestablish trabecular connectivity if therapeutic intervention occurs after the trabecular connectivity has been lost.

Trabecular architecture in women and men of similar bone mass with and without vertebral fracture: I. Two-dimensional histology

While osteoporosis is characterized by a low bone mass there is a well-recognized overlap in bone mineral density (BMD) measurements between groups of subjects with and without vertebral fracture. To investigate whether differences in trabecular architecture may contribute to the presence or absence of fractures independent of the bone mass, fracture and nonfracture groups matched for age, gender, and BMD were assembled. Transiliac biopsies and corresponding lumbar spine BMD measurements from 31 women and 16 men with vertebral fracture were compared with those from 22 women and 11 men without fracture. Lumbar BMD (L1-4) was measured using a Hologic 2000 densitometer. The lumbar BMD was similar in women with and without fracture (0.63 g/cm(3) +/- 0.10 SD and 0.71 g/cm(3) +/- 0.17 SD, n.s.) and in men with and without fracture (0.72 g/cm(3) +/- 0.12 SD and 0.76 g/cm(3) +/- 0.17 SD, n.s.). Undecalcified iliac crest biopsy sections, 8 microm thick, were analyzed for remodeling variables and trabecular architecture using OsteoMeasure and TAS image analysis systems. No significant difference was found in either gender between fracture and nonfracture groups in percent bone volume (mean 10% in all groups), or in the wide range of remodeling and architectural variables measured, including the trabecular width, number, and separation, mean trabecular plate density and fractal dimension, as well as several indirect indices of connectivity including the node:terminus ratio, marrow star volume, and trabecular pattern factor. On the basis of this evidence it was concluded that there is no difference in the trabecular architecture between patients with crush fracture and controls when account is taken of bone mass. This suggests that microanatomical disruption is a predictable intrinsic feature of bone loss. However, there remains the possibility that the two-dimensional character of the structural deterioration measured indirectly is not sufficiently sensitive for the complex cancellous system. This is considered further in part II.

Quantitative analysis of three-dimensional complexity and connectivity changes in trabecular microarchitecture in relation to aging, menopause, and inflammation

There are several types of bone loss besides that associated with normal aging, eg, that associated with the menopause, and that associated with chronic inflammation, and these are considered to be caused by different mechanisms. The microarchitecture that results from these different bone-loss mechanisms would not be the same. The purpose of this study was to investigate differences in the three-dimensional trabecular microarchitecture in various types of osteopenia, using microcomputed tomography (Micro-CT). Thirty-five Fisher 344 rats were divided into five groups (control, young, senile, ovariectomized [OVX], and inflammation-mediated osteopenia [IMO]) and distal femoral metaphysis was scanned by Micro-CT to nondestructively acquire a 3-D CT stack consisting of 50 consecutive slices at a spatial resolution of 26 microm. The volume of interest, consisting of the secondary spongiosa, was prepared to analyze the 3-D trabecular microarchitecture. A parametric analysis was carried out using bone volume fractions, fractal dimensions, and the first Betti number in order to quantitatively express the mass, complexity, and connectivity of the trabecular microarchitecture. Complexity tended to decrease with age, and decreased significantly in estrogen deficiency-induced and inflammation-mediated osteopenia. Connectivity did not appear to change with aging, but was significantly decreased in estrogen deficiency-induced and inflammation-mediated osteopenia. There was no significant difference between the OVX and the IMO groups.

Apoptosis and osteoporosis

During normal bone remodeling, the rate of supply of new osteoblasts and osteoclasts and the timing of the death of osteoclasts, osteoblasts, and osteocytes by apoptosis are critical determinants of the initiation of new BMUs and the extension or reduction of the lifetime of existing ones. Disruption of the fine balance among these processes may be an important mechanism behind the deranged bone turnover found in most metabolic disorders of the adult skeleton. Like most armies, the amount 5 of work done by bone cells is far more dependent on numbers than vigor. Therapeutic agents that alter the prevalence of apoptosis of osteoblasts and osteoclasts can correct the imbalance in cell numbers that is the basis of the diminished bone mass and increased risk of fractures in osteoporosis.

Computerized analysis of radiographic bone patterns: effect of imaging conditions on performance

We are developing computerized methods for characterizing the bone texture pattern from digitized skeletal radiographs. For this method to be useful clinically, it must be able to distinguish between weak and strong bone under the range of exposure conditions potentially encountered in the clinical setting. In this study, we examined the effect of exposure conditions on Fourier-based texture features. Thirty-four femoral specimens from total hip arthroplasties were radiographed multiple times under different exposure conditions. The specimens underwent mechanical strength testing from which load to failure values were obtained. The performance of the texture features were investigated in the task of distinguishing between strong and weak bone as characterized by the load to failure values. The texture features showed no dependence upon focal spot size of the x-ray tube or magnification. The texture features did show a dependence with relative exposure, peak kilovoltage, and amount of scattering material.

Issues of threshold selection when determining the fractal dimension in HRCT slices of lumbar vertebrae

The box counting dimension is a frequently applied tool for the classification of trabecular bone structure. The algorithm requires a binarization of the gray value data, for example that acquired by high resolution CT (HRCT). We recently proposed a method to eliminate bone mineral density (BMD) by applying a linear normalization scheme. Further consideration has shown that full BMD independence has not been achieved, and the structural parameter proposed was therefore difficult to interpret. In this study we present an alternative approach to obtain a structural parameter that is independent of BMD. HRCT volume data was acquired on 21 lumbar vertebrae from five cadavers. In the segmented spongiosa, thresholding was based on different quantiles of the gray value histogram, yielding invariance over linear and non-linear transformations. Thresholding at high gray value levels (80% quantile) shows the highest level of significance when discriminating between osteoporotic and non-osteoporotic cases. As an addition to the measurement of BMD alone, the determination of structural properties allows an improvement of the assessment of the individual fracture risk.

Computerized radiographic texture measures for characterizing bone strength: a simulated clinical setup using femoral neck specimens

We are investigating computerized methods to ultimately characterize bone trabecular pattern from clinical skeletal radiographs. In this paper, we present a "phantom" for potential use in the development and evaluation of computerized methods for characterizing radiographic trabecular patterns and ultimately bone strength. Femoral neck specimens were excised during total hip arthroplasties from subjects exhibiting a range of diseases. To mimic the femoral neck in vivo, a "simulated clinical" setup was implemented in which specimens were exposed under conditions that yielded radiographs similar in appearance to standard pelvis radiographs. Fourier-based and fractal-based texture measures were used in the computer analysis; including RMS variation, first moment of the power spectrum, angular-dependent forms of these measures, and fractal dimension. The texture measures obtained from the "simulated clinical" specimen films correlated modestly with those from direct exposure "verification" films of the specimens (r= 0.59-0.69; p<0.0001). From our study, we conclude that the femoral neck specimen "phantoms" may be useful in the development and evaluation of computerized methods for analyzing bone trabecular patterns from skeletal radiographs. The use of a phantom that simulates the clinical radiographic examination allows for repeat exposures without the concern of excessive radiation exposure to a patient.

Fractal analysis: an objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri

OBJECTIVES

Fractal geometry is a tool used to characterize irregularly shaped and complex figures. It can be used not only to generate biological structures (e.g., the human renal artery tree), but also to derive parameters such as the fractal dimension in order to quantify the shapes of structures. As such, it allows user-independent evaluation and does not rely on the experience level of the examiner.

METHODS

We applied a box-counting algorithm to determine the fractal dimension of atypical nuclei in dysplastic cervical epithelium. An automatic algorithm was used to determine the fractal dimension of nuclei in order to prevent errors from manual segmentation. Four groups of patients (CIN 1-3 and control) with 10 subjects each were examined. In total, the fractal dimensions of 1200 nuclei were calculated.

RESULTS

We found that the fractal dimensions of the nuclei increased as the degree of dysplasia increased. There were significant differences between control and atypical nuclei found by an analysis of variance. Atypical nuclei associated with CIN 1, CIN 2, and CIN 3 also differed significantly among these groups.

CONCLUSION

We conclude that the fractal dimension is a valuable tool for detecting irregularities in atypical nuclei of the cervix uteri and thus allows objective nuclear grading.

Computer simulations for the optimization of magnetic resonance phase imaging applied in the study of trabecular bone

A new technique for the evaluation of bone trabeculation using magnetic resonance (MR) phase images has been recently presented. This technique calculates the phase variance in a region of interest (ROI) on the phase images of a gradient echo sequence. In this study, a computer program was developed which simulates the phase distribution in gradient echo acquired phase images of a structure that mimics trabecular bone, consisting of a three-dimensional connected network of orthogonal bone struts. Several tests were performed in order to assess the influence of imaging parameters such as the echo time, the pixel size and the slice width on phase variance. The results from this work show that with selection of appropriate imaging parameters, phase variance strongly reflects variations in trabecular bone density. Representative MR experiments were performed in the distal radius to verify the simulation results.

Fractal analysis of radiographs: assessment of trabecular bone structure and prediction of elastic modulus and strength

The purpose of this study was to determine whether fractal dimension of radiographs provide measures of trabecular bone structure which correlate with bone mineral density (BMD) and bone biomechanics, and whether these relationships depend on the technique used to calculate the fractal dimension. Eighty seven cubic specimen of human trabecular bone were obtained from the vertebrae and femur. The cubes were radiographed along all three orientations--superior-inferior (SI), medial-lateral (ML), and anterior-posterior (AP), digitized, corrected for background variations, and fractal based techniques were applied to quantify trabecular structure. Three different techniques namely, semivariance, surface area, and power spectral methods were used. The specimens were tested in compression along three orientations and the Young's modulus (YM) was determined. Compressive strength was measured along the SI direction. Quantitative computed tomography was used to measure trabecular BMD. High-resolution magnetic-resonance images were used to obtain three-dimensional measures of trabecular architecture such as the apparent bone volume fraction, trabecular thickness, spacing, and number. The measures of trabecular structure computed in the different directions showed significant differences (p<0.05). The correlation between BMD, YM, strength, and the fractal dimension were direction and technique dependent. The trends of variation of the fractal dimension with BMD and biomechanical properties also depended on the technique and the range of resolutions over which the data was analyzed. The fractal dimension showed varying trends with bone mineral density changes, and these trends also depended on the range of frequencies over which the fractal dimension was measured. For example, using the power spectral method the fractal dimension increased with BMD when computed over a lower range of spatial frequencies and decreased for higher ranges. However, for the surface area technique the fractal dimension increased with increasing BMD. Fractal measures showed better correlation with trabecular spacing and number, compared to trabecular thickness. In a multivariate regression model inclusion of some of the fractal measures in addition to BMD improved the prediction of strength and elastic modulus. Thus, fractal based texture analysis of radiographs are technique dependent, but may be used to quantify trabecular structure and have a potentially valuable impact in the study of osteoporosis.

Comparison of eight histomorphometric methods for measuring trabecular bone architecture by image analysis on histological sections

Osteoporosis is defined as a disease characterized by low bone mass and microarchitectural deterioration of trabecular bone leading to enhanced bone fragility. Various histomorphometric methods have been described to measure bone architecture on histological sections. However, not all of the methods are strictly equivalent and some of them appear able to detect differences earlier in the course of the disease. We have compared 8 histomorphometric methods known to characterize the architecture of trabecular bone in 154 male osteoporotic patients. Measurements were done on transiliac bone biopsies: Trabecular number, thickness, and separation (Tb.N, Tb.Th, Tb.Sp); Trabecular Bone Pattern Factor (TBPf); Euler-Poincare's number (E); Interconnectivity Index (ICI); strut analysis of the trabecular network with the ratio of nodes/free-end (N/F); star volume of the bone marrow (V*m.space) and trabeculae (V*Tb) and the Kolmogorov fractal dimension of the trabecular boundaries (D). Relationships between the various architectural parameters were studied by hierarchical cluster analysis. Linear, hyperbolic, and exponential correlations were found between trabecular bone volume (BV/TV) and architectural parameters. Cluster analysis demonstrates the link between these architectural parameters. ICI, E, and TBPf, which reflect the amount of open/closed marrow cavities clustered together and appeared related to Tb.Sp, V*m.space which are indicators of the mean size of marrow cavities. Tb.Th, V*Tb and N/F flocked together as they reflect the trabecular size. Tb.N and D segregated together and seemed to best describe the trabecular network complexity. These histomorphometric techniques are correlated but correlations may be linear or nonlinear. Several histomorphometric techniques need to be used in parallel to appreciate the pathophysiological mechanisms of osteoporotic states.

A comparison of porosity, fabric and fractal dimension as predictors of the Young's modulus of equine cancellous bone

The purpose of this study was to compare the structural parameters of fabric and fractal dimension as predictors of the Young's modulus of equine cancellous bone. Eight 15 mm cubes of cancellous bone were obtained from three equine third metacarpal bones. Young's modulus was determined for the three orthogonal directions. The fabric and fractal dimension were calculated for each of the six exposed faces of each cube. Fractal dimension plus porosity provided a higher explanatory power for Young's modulus (R2 = 78.7%. P < 0.0001) than fabric plus porosity (R2 = 69.2%, P < 0.0001). Fractal dimension was also significantly correlated with fabric (R2 = 53.8%, P < 0.0001). Although this novel method for combining fractal dimension data into a pseudo-directionally dependent predictor of Young's modulus requires further validation over a greater range of porosities and differing cancellous bone tissues, its potential has been demonstrated.

Biomechanical properties of human os calcanei: relationships with bone density and fractal evaluation of bone microarchitecture

The relationship between bone strength and bone mass is well established. The link between trabecular microarchitecture and biomechanical properties has been less extensively explored. To address this question, we have tested the mechanical behaviour of calcaneus bone samples and investigated the correlations between mechanical properties on the one hand, bone density and fractal analysis of microarchitecture on the other hand. Mechanical properties of 43 human os calcanei were determined by uniaxial compression testing of samples from tuber calcanei. Ash density, bulk density and dual energy X-ray absorptiometry of the samples were measured. Fractal analysis of the trabecular bone on calcaneus radiographs was performed by two estimators derived from the fractional Brownian motion model. The mechanical properties of human os calcis were found to correlate with age and density measurements. Fractal parameters derived from the bone texture analysis showed weaker but significant correlations with bone strength. Fractal analysis of texture could account in part for the variations of bone strength, but in this study cannot explain better than density the mechanical properties of trabecular bone. Nevertheless, it provides a non-invasive means of assessing molecular bone microarchitecture.

Fractal properties of cancellous bone of the iliac crest in vertebral crush fracture

Fractal analysis is a method for describing complex shapes, including the cancellous structure of bone. It describes the surface texture and form of individual trabecular profiles and the overall cancellous structure. Sixty-four postmenopausal women with symptoms of back pain were referred for investigation for osteoporosis. The patients were divided into two groups for comparison: vertebral crush fracture (n = 31, mean age 68.58 +/- 6.47 years), and no vertebral crush fracture (n = 33, mean age 63.36 +/- 7.21 years). Cores of cancellous bone, 3 mm in diameter, were taken from the iliac crest and sectioned. A box-counting method implemented on an image analyzer was used to measure the fractal dimension. Three fractal dimensions describing trabecular surface texture (fractal 1), trabecular shape (fractal 2), and trabecular arrangement (fractal 3) were measured, indicating that cancellous bone has sectional self-similarity. Conventional histomorphometry was also performed on the samples. The results show that fractal 2 is significantly lower in the vertebral crush fracture group than in the nonfracture group (1.15 +/- 0.10 < 1.23 +/- 0.090, p < 0.0013). The histomorphometric analysis shows that bone surface total volume (p < 0.0002), trabecular number (p < 0.0001), and osteoid surface bone surface (p < 0.028) are significantly lower in the fracture group than the nonfracture group. Eroded surface/bone surface (p < 0.056) follows this trend, whereas trabecular separation (p < 0.001) is significantly higher in the fracture group than in the nonfracture group. Fractal 1 and fractal 3 were not significantly different between study groups. The fractal dimension detects changes in the cancellous architecture and gives information about iliac bone transformation in postmenopausal women with vertebral fracture.