Effect of BaTiO3 Filler Modification with Multiwalled Carbon Nanotubes on Electric Properties of Polymer Nanocomposites.

Two ranges of dielectric permittivity (k) increase in polymer composites upon the modification of BaTiO3 filler with multiwalled carbon nanotubes (MWCNTs) are shown for the first time. The first increase in permittivity is observed at low MWCNT content in the composite (approximately 0.07 vol.%) without a considerable increase in dielectric loss tangent and electrical conductivity. This effect is determined by the intensification of filler-polymer interactions caused by the nanotubes, which introduce Brønsted acidic centers on the modified filler surface and thus promote interactions with the cyanoethyl ester of polyvinyl alcohol (CEPVA) polymer binder. Consequently, the structure of the composites becomes more uniform: the permittivity increase is accompanied by a decrease in the lacunarity (nonuniformity) of the structure and an increase in scale invariance, which characterizes the self-similarity of the composite structure. The permittivity of the composites in the first range follows a modified Lichtenecker equation, including the content of Brønsted acidic centers as a parameter. The second permittivity growth range features a drastic increase in the dielectric loss tangent and conductivity corresponding to the percolation effect with the threshold at 0.3 vol.% of MWCNTs.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens.

Introduction: Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks. Methods: In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach. Results: The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05). Conclusions: The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

Box-Counting Fractal Analysis: A Primer for the Clinician.

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

The Fractal Geometry of the Brain: AnOverview.

The first chapter of this book introduces some history, philosophy, and basic concepts of fractal geometry and discusses how the neurosciences can benefit from applying computational fractal-based analysis. Further, it compares fractal with Euclidean approaches to analyzing and quantifying the brain in its entire physiopathological spectrum and presents an overview of the first section of this book as well.

Optical coherence tomography angiography macular biomarkers of peripheral retinal ischemia in diabetic macular edema: secondary endpoints from the clinical study "FOVEA".

PURPOSE: To investigate the relationship between the macular values of fractal dimension (FD) and lacunarity (LAC) on optical coherence tomography angiography (OCTA) images and the presence of peripheral retina non-perfusion areas (NPAs) on fluorescein angiography (FA) in patients with treatment-naïve diabetic macular edema (DME). METHODS: Fifty patients with treatment-naïve DME underwent a full ophthalmic examination, including best-corrected visual acuity measurement, FA, spectral-domain optical coherence tomography, and OCTA. Specifically, FA was performed to detect the presence of retinal NPAs, whereas fractal OCTA analysis was used to determine macular FD and LAC values at the level of the superficial and deep capillary plexus (SCP and DCP). FA montage frames of the posterior pole and peripheral retina, as well as macular OCTA slabs of the SCP and DCP, were obtained. RESULTS: Thirty (60%) eyes with FA evidence of peripheral retinal NPAs in at least one quadrant showed significantly lower FD and higher LAC in both SCP and DCP, when compared with eyes presenting a well-perfused peripheral retina. Furthermore, macular FD and LAC values were found to be significantly associated with the extent of retinal NPAs. CONCLUSIONS: Macular FD and LAC of both SCP and DCP seem to be strongly associated with the extent of peripheral retinal NPAs, thus suggesting that may be useful predictive biomarkers of peripheral ischemia in treatment-naïve DME eyes.

Quantitative analysis of the correlation between gel strength and microstructure of shrimp surimi gel induced by dense phase carbon dioxide.

The impact of treatment pressure, temperature and time of DPCD on the Pacific White Shrimp (Litopenaeus vannamei) surimi gel properties was studied and compared with the conventional heat treatment. The gel strength, crosslinking degree, and microstructure of shrimp surimi gels were investigated. Quantitative microstructural characteristics were investigated to elucidate the changes in microstructure during the formation of gel induced by DPCD. With increased DPCD treatment setting conditions, the gel strength and crosslinking degree of shrimp surimi gel significantly improved (P < 0.05) with similar variation trends. Quantitative microstructural analysis revealed that the fractal dimension (Df) and the pore equivalent diameter of gel microstructure increased with the increase of DPCD treatment conditions. The lacunarity decreased and then increased, whereas pore number increased and decreased. According to the microstructural characteristics results, the surimi gel with 51.48 % degree of crosslinking induced at 25 MPa, 50˚C, and 60 min showed the most complex and homogeneous microstructure with the highest (Df), smaller lacunarity, an average pore equivalent diameter, and a larger pore number. The correlation analysis demonstrated that the crosslinking degree was strongly positively correlated with the gel strength. The Df, pore equivalent diameter and number of pores significantly positively correlated with the crosslinking degree, whereas the lacunarity strongly negatively correlated with the crosslinking degree. The present study showed that the DPCD treatment with a crosslinking degree of 51.48 % is the most optimum condition for better gel formation. The study could provide a theoretical basis for processing shrimp surimi with improved gel properties.

A highly generalized classifier for osteoporosis radiography based on multiscale fractal, lacunarity, and entropy distributions.

Background: Osteoporosis is a common degenerative disease with high incidence among aging populations. However, in regular radiographic diagnostics, asymptomatic osteoporosis is often overlooked and does not include tests for bone mineral density or bone trabecular condition. Therefore, we proposed a highly generalized classifier for osteoporosis radiography based on the multiscale fractal, lacunarity, and entropy distributions. Methods: We collected a total of 104 radiographs (92 for training and 12 for testing) of lumbar spine L4 and divided them into three groups (normal, osteopenia, and osteoporosis). In parallel, 174 radiographs (116 for training and 58 for testing) of calcaneus from health and osteoporotic fracture groups were collected. The texture feature data of all the radiographs were pulled out and analyzed. The Davies-Bouldin index was applied to optimize hyperparameters of feature counting. Neighborhood component analysis was performed to reduce feature dimension and increase generalization. A support vector machine classifier was trained with only the most effective six features for each binary classification scenario. The accuracy and sensitivity performance were estimated by calculating the area under the curve. Results: Interpretable feature trends of osteoporotic pathological changes were depicted. On the spine test dataset, the accuracy and sensitivity of binary classifiers were 0.851 (95% CI: 0.730-0.922), 0.813 (95% CI: 0.718-0.878), and 0.936 (95% CI: 0.826-1) for osteoporosis diagnosis; 0.721 (95% CI: 0.578-0.824), 0.675 (95% CI: 0.563-0.772), and 0.774 (95% CI: 0.635-0.878) for osteopenia diagnosis; and 0.935 (95% CI: 0.830-0.968), 0.928 (95% CI: 0.863-0.963), and 0.910 (95% CI: 0.746-1) for osteoporosis diagnosis from osteopenia. On the calcaneus test dataset, they were 0.767 (95% CI: 0.629-0.879), 0.672 (95% CI: 0.545-0.793), and 0.790 (95% CI: 0.621-0.923) for osteoporosis diagnosis. Conclusion: This method showed the capacity of resisting disturbance on lateral spine radiographs and high generalization on the calcaneus dataset. Pixel-wise texture features not only helped to understand osteoporosis on radiographs better but also shed new light on computer-aided osteopenia and osteoporosis diagnosis.

Measuring Drug Therapy Effect on Osteoporotic Fracture Risk by Trabecular Bone Lacunarity: The LOTO Study.

An MRI method providing one parameter (TBLß: trabecular-bone-lacunarity-parameter-ß) that is sensitive to trabecular bone architecture (TBA) changes with aging and osteoporosis is under study as a new tool in the early diagnosis of bone fragility fracture. A cross-sectional and prospective observational study (LOTO: Lacunarity Of Trabecular bone in Osteoporosis) on over-50s women, at risk for bone fragility fracture, was designed to validate the method. From the baseline data, we observed that in women with prevalent vertebral fractures (VF+), TBA was differently characterized by TBLß when osteoporosis treatment is considered. Here we verify the potential of TBLß as an index of osteoporosis treatment efficacy. Untreated (N = 156) and treated (N = 123) women were considered to assess differences in TBLß related to osteoporosis treatment. Prevalent VFs were found in 31% of subjects, 63% of which were under osteoporosis medications. The results show that TBLß discriminates between VF+ and VF- patients (p = 0.004). This result is mostly stressed in untreated subjects. Treatment, drug therapy in particular (89% Bisphosphonates), significantly counteracts the difference between VF+ and VF- within and between groups: TBLß values in treated patients are comparable to untreated VF- and statistically higher than untreated VF+ (p = 0.014) ones. These results highlight the potential role of TBLß as an index of treatment efficacy.

Demystifying neuroblastoma malignancy through fractal dimension, entropy, and lacunarity.

PURPOSE: Neuroblastoma is a pediatric solid tumor with a prognosis associated with histology and age of the patient, which are the parameters of the well-established current classification (Shimada classification). Despite the development of new treatment options, the prognosis of high-risk neuroblastoma patients is still poor. Therefore, there is a continuous need to stratify the children suffering from this tumor. A mathematical and computational approach is proposed to enable automatic and precise cancer diagnosis on the histological slide. METHODS: We targeted the complexity of neuroblastoma by calculating its image entropy (S), fractal dimension (FD), and lacunarity (λ) in a combined mathematical code. First, we tested the proposed method for patient-derived glioma images. It allowed distinguishing between normal brain tissue, grade II, and grade III glioma, which harbor different outcomes. RESULTS: In neuroblastoma, our analysis of image's FD, S, and λ combined with a machine learning algorithm automatically predicted tumor malignancy with a receiver operating characteristic curve of 0.82. FD, S, and λ distinguish between neuroblastoma and ganglioneuroma, but they only partially differentiate between the normal samples and the other classes. Ganglioneuroma, the most differentiated form, and poorly-differentiated neuroblastoma display different values of FD, S, and λ. CONCLUSIONS: FD, S, and λ of imaging recognize groups in neuroblastic tumors. We suggest that future studies including these features may challenge the current Shimada classification of neuroblastoma with categories of favorable and unfavorable histology. It is expected that this methodology could trigger multicenter studies and potentially find practical use in the clinical setting of children's hospitals worldwide.

The Fractal Viewpoint of Tumors and Nanoparticles.

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Application of Lacunarity for Quantification of Single Molecule Localization Microscopy Images.

The quantitative analysis of datasets achieved by single molecule localization microscopy is vital for studying the structure of subcellular organizations. Cluster analysis has emerged as a multi-faceted tool in the structural analysis of localization datasets. However, the results it produces greatly depend on the set parameters, and the process can be computationally intensive. Here we present a new approach for structural analysis using lacunarity. Unlike cluster analysis, lacunarity can be calculated quickly while providing definitive information about the structure of the localizations. Using simulated data, we demonstrate how lacunarity results can be interpreted. We use these interpretations to compare our lacunarity analysis with our previous cluster analysis-based results in the field of DNA repair, showing the new algorithm's efficiency.

Fractal methods applied to the seminiferous lumen images can quantify testicular changes induced by heat stress.

Male infertility affects many couples around the world and can be related to environmental factors such as exposure to high temperatures. Even so, automated methods evaluating the seminiferous tubules to detect testicular damage are still scarce. In search of new approaches to automation in the microscopic analysis of the testis; the present study used the fractal dimension, lacunarity, multifractality and quantitative morphometry to quantify changes in microphotographs of the seminiferous lumen in testicles reversibly damaged by heat stress (43 °C, 12 min). The parameters fractal dimension, lacunarity, multifractality (Dq and α), perimeter, feret and circularity were able to detect changes in the seminiferous lumen at 7, 15 and 30 days after the testicular damage. These methods also detected the recovery of spermatogenesis at 60 days after heat stress. Area, f(α), centroid X and Y, roundness, rectangle height and width were unable to detect changes caused by heat stress. In conclusion, computer assisted methods applied to the seminiferous lumen images can be a useful new viewpoint to analyze microscopic changes in the testicles, a fast low-cost tool to assist in the automated quantification of testicular damage.

The Association of Fractal Dimension with Vascularity and Clinical Outcomes in Glioblastoma.

BACKGROUND: Growing evidence indicates fractal analysis (FA) has potential as a computational tool to assess tumor microvasculature in glioblastoma (GBM). As fractal parameters of microvasculature have shown to be reliable quantitative biomarkers in brain tumors, there has been similar success in measuring the architecture of tumor tissue using FA in other tumor types. However, evaluating fractal parameters of tissue structure in relation to the microvasculature has not yet been implemented in GBM. We aimed to assess the utility of this methodology in quantifying structural characteristics of GBM cytoarchitecture and vascularity by correlating fractal parameters with gene expression. METHODS: Formalin-fixed paraffin-embedded specimens were retrospectively collected from 43 patients following resection of a newly diagnosed GBM; 4 normal brain specimens were obtained from epilepsy surgeries as controls. Tumor samples were processed using FA employing a software-based box-counting method algorithm and custom messenger RNA expression assays. Fractal parameters were then correlated with clinical features, outcomes, and a panel of 92 genes associated with vascularity and angiogenesis. RESULTS: Statistical analysis demonstrated that fractal-based indices were not adequate parameters for distinction of GBM cytoarchitecture compared with normal brain specimens. Correlation analysis of our gene expression findings suggested that hematoxylin and eosin-based FA may have adequate sensitivity to detect associations with vascular gene expression. CONCLUSIONS: The combination of neuropathological assessment and histology does not provide optimized data for FA in GBM. However, an association between FA and gene expression in GBM of genes pertaining to cytoarchitecture and angiogenesis warrants further investigation.

Distinct fatty acid redistribution and textural changes in the brain tissue upon the static magnetic field exposure.

We observed different outcomes upon the subacute exposure to the 128 mT highly homogeneous static magnetic field (SMF) when its orientation was (i) aligned with the vertical component of the geomagnetic field; (ii) in the opposite direction. We employed the fatty acids (FA) composition and digital image analyses (DIA) to provide insights into the underlying processes and examine the possible weak SMF effects. Swiss-Webster male mice were whole-body exposed for 1 h/day over five days. Brain tissue's thin liquid chromatography resulted in brain FA composition, indicating a possible sequence of changes due to the SMF exposure. Quantitative DIA accurately assessed different image parameters. Delicate textural changes were revealed in the group where pathohistological or biochemical alterations have not been detected. DIA-based biological markers seem to be very promising for studying delicate tissue changes, which results from the high sensitivity and wide availability of DIA.

Fractal analysis in the quantification of medical imaging associated with multiple sclerosis pathology.

BACKGROUNDS: Multiple sclerosis (MS) is an inveterate phlogistic situation characterized by focal and vaguely diffusive de-myelination and neurodegeneration, in the sphere of central nervous system (CNS). The brain's chronic inflammatory reaction includes astrocyte stimulation and microglial motivation, as well as macrophages marginal conscription. This lasting serious soreness of the brain is connected with neurodegeneration period and disability advance. METHODS: The present study is considering two main purposes as follows. Primarily, to apply the fractal analysis in the idea of documenting the fractals dominance at all stages of the nervous system hierarchy, giving faith to the precept of their funciar relevancy. Secondly, to take into account the problems unresolved of the thorough connections between self-organized criticality concept and self-similarity notion. More precisely, in reality we will obtain information about the fractal size and lacunarity of magnetic resonance imaging (MRI), on the areas of interest of the brain, rich in microglial cells with fringes from peripheral macrophages cells. RESULTS: This approach will play a decisive role in the action of detecting neural disabilities, such as in particular multiple sclerosis cortical onset, the final goal of our investigation. The diagnosis is based on interpretation of both histological sample pictures and images obtained by nuclear magnetic resonance. Using fractal analysis, we have calculated, for each image separately, both the fractal dimension and the lacunarity, as an objective quantitative measure of the demyelinating action. CONCLUSIONS: For three histopathological samples on glial cells, with visible erosions, the fractal dimension has value over 1.89 and the lacunarity value is between 0.050 and 0.079. In the gray level stages of the studied MRI pictures, the fractal dimension is above the value of 1.7 and the lacunarity is between the values of 0.0286 and 0.0393.

Morphological, fractal, and textural features for the blood cell classification: the case of acute myeloid leukemia.

Microscopic examination of stained peripheral blood smears is, nowadays, an indispensable tool in the evaluation of patients with hematological and non-hematological diseases. While a rapid automated quantification of the regular blood cells is available, recognition and counting of immature white blood cells (WBC) still relies mostly on the microscopic examination of blood smears by an experienced observer. Recently, there are efforts to improve the prediction by various machine learning approaches. An open dataset collection including the recently digitalized single-cell images for 200 patients, from peripheral blood smears at 100 × magnification, was used. We studied different morphological, fractal, and textural descriptors for WBC classification, with an aim to indicate the most reliable parameters for the recognition of certain cell types. Structural properties of both the mature and non-mature leukocytes obtained from (i) acute myeloid leukemia patients, or (ii) non-malignant controls, were studied in depth, with a sample size of about 25 WBC per group. We quantified structural and textural differences and, based on the statistical ranges of parameters for different WBC types, selected eight features for classification: Cell area, Nucleus-to-cell ratio, Nucleus solidity, Fractal dimension, Correlation, Contrast, Homogeneity, and Energy. Classification Precision of up to 100% (80% on average) was achieved.

Fractal dimension and lacunarity analysis of mandibular bone on digital panoramic radiographs of tobacco users.

Background. This study aimed to evaluate and compare changes in the mandibular trabecular bone pattern using the fractal dimension (FD) and lacunarity analysis in tobacco users with healthy controls. Methods. This study was carried out on digital panoramic radiographs of 225 subjects divided into three groups: smokeless tobacco users (SLTs), smokers, and control (n=75). ImageJ program with FracLac plugin was used to assess the FD and lacunarity of mandibular trabecular bone on the digital panoramic radiographs. Results. The differences in the mean FD values of the study and control groups were statistically significant (P < 0.001). Mean FD was lower in the case groups than the control group, with SLTs having the least FD value. A significant difference in lacunarity was noted between SLTs and controls (P < 0.001). On the contrary, there was no significant difference in lacunarity between smokers and controls. Conclusions. FD values were lower in tobacco users, suggesting that tobacco users have a less complex trabecular bone pattern than healthy controls. Higher lacunarity values in SLTs indicated a more heterogeneous bone pattern. These findings signify that FD and lacunarity analysis on digital panoramic radiographs can serve as promising predictive tools to assess bone quality for osteoporotic changes in tobacco users, thereby facilitating prompt referral for further management.

Morphological characterization of Etv2 vascular explants using fractal analysis and atomic force microscopy.

The rapid engraftment of vascular networks is critical for functional incorporation of tissue explants. However, existing methods for inducing angiogenesis utilize approaches that yield vasculature with poor temporal stability or inadequate mechanical integrity, which reduce their robustness in vivo. The transcription factor Ets variant 2 (Etv2) specifies embryonic hematopoietic and vascular endothelial cell (EC) development, and is transiently reactivated during postnatal vascular regeneration and tumor angiogenesis. This study investigates the role for Etv2 upregulation in forming stable vascular beds both in vitro and in vivo. Control and Etv2+ prototypical fetal-derived human umbilical vein ECs (HUVECs) and adult ECs were angiogenically grown into vascular beds. These vessel beds were characterized using fractal dimension and lacunarity, to quantify their branching complexity and space-filling homogeneity, respectively. Atomic force microscopy (AFM) was used to explore whether greater complexity and homogeneity lead to more mechanically stable vessels. Additionally, markers of EC integrity were used to probe for mechanistic clues. Etv2+ HUVECs exhibit greater branching, vessel density, and structural homogeneity, and decreased stiffness in vitro and in vivo, indicating a greater propensity for stable vessel formation. When co-cultured with colon tumor organoid tissue, Etv2+ HUVECs had decreased fractal dimension and lacunarity compared to Etv2+ HUVECs cultured alone, indicating that vessel density and homogeneity of vessel spacing increased due to the presence of Etv2. This study sets forth the novel concept that fractal dimension, lacunarity, and AFM are as informative as conventional angiogenic measurements, including vessel branching and density, to assess vascular perfusion and stability.

Fractal lacunarity of trabecular bone in vertebral MRI to predict osteoporotic fracture risk in over-fifties women. The LOTO study.

BACKGROUND: Osteoporotic fractures are a major cause of morbidity in the elderly. Menopausal women represent the population with the highest risk of early osteoporosis onset, often accompanied by vertebral fractures (VF). Bone mineral density (BMD) is commonly assessed by dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnosis; however, BMD alone does not represent a significant predictor of fracture risk. Bone microarchitecture, instead, arises as a determinant of bone fragility independent of BMD. High-resolution magnetic resonance imaging (MRI) is an effective noninvasive/nonionizing tool for in vivo characterisation of trabecular bone microarchitecture (TBA). We have previously set up an MRI method able to characterise TBA changes in aging and osteoporosis by one parameter, trabecular bone lacunarity parameter ß (TBLß). Fractal lacunarity was used for TBA texture analysis as it describes discontinuity of bone network and size of bone marrow spaces, changes of which increase the risk of bone fracture. This study aims to assess the potential of TBLß method as a tool for osteoporotic fracture risk. METHODS: An observational, cross-sectional, and prospective study on over-50s women at risk for VF was designed. TBLß, our index of osteoporotic fracture risk, is the main outcome measure. It was calculated on lumbar vertebra axial images, acquired by 1.5 T MRI spin-echo technique, from 279 osteopenic/osteoporotic women with/without prior VF. Diagnostic power of TBLß method, by Receiver Operating Characteristics (ROC) curve and other diagnostic accuracy measurements were compared with lumbar spine DXA-BMD. RESULTS: Baseline results show that TBLß is able to discriminate patients with/without prevalent VF (p = 0.003). AUC (area under the curve from ROC) is 0.63 for TBLß, statistically higher (p = 0.012) than BMD one (0.53). Contribution of TBLß to prevalent VF is statistically higher (p < 0.001) than BMD (sensitivity: 66% vs. 52% respectively; OR: 3.20, p < 0.0001 for TBLß vs. 1.31, p = 0.297 for BMD). Preliminary 1-year prospective results suggest that TBA contribution to incident VF is even higher (sensitivity: 73% for TBLß vs. 55% for BMD; RR: 3.00, p = 0.002 for TBLß vs. 1.31, p = 0.380 for BMD). CONCLUSION: Results from this study further highlight the usefulness of TBLß as a biomarker of TBA degeneration and an index of osteoporotic fracture risk.

Prognostic Significance of Lacunarity in Preoperative Biopsy of Colorectal Cancer.

The quantity and quality of preoperative material in colorectal cancer is often limiting factor in determination of risk factors and therapy planning. The most important negative prognostic factors are intravascular and perineural invasion, as well as tumor budding. Usually, the only parameter available in preoperative biopsy is tumor budding. However, the growing body of evidence suggests that cancer differentiation based on the poorly differentiated clusters has better prognostic value. The limiting factor in applying of these new parameters is reproducible, simple, cheap and fast method of their determination. In this paper we investigated the prognostic value of lacunarity, determined in preoperative biopsy. Lacunarity is a measure of spatial heterogeneity (inhomogeneity) in an image. It quantifies how objects fill the space, and enables analysis of gaps distribution, homogeneity of gaps, and presence of structures. It was shown that lacunarity and the total number of buds could be combined in a model which clearly divides colorectal cancer patients in low, medium and high risk subgroups. The paper also points out that the quantitative numerical methods are superior to semiquantitative methods, and that individual methods should be combined using algorithms to obtain a more accurate prediction. Because the study described is designed as a pilot study, verification is needed on a larger sample of patients from independent researchers.