The morphological complexity of cells and tissues, whether normal or pathological, is characterized by two primary attributes: Irregularity and self-similarity across different scales. When an object exhibits self-similarity, its shape remains unchanged as the scales of measurement vary because any part of it resembles the whole. On the other hand, the size and geometric characteristics of an irregular object vary as the resolution increases, revealing more intricate details. Despite numerous attempts, a reliable and accurate method for quantifying the morphological features of gastrointestinal organs, tissues, cells, their dynamic changes, and pathological disorders has not yet been established. However, fractal geometry, which studies shapes and patterns that exhibit self-similarity, holds promise in providing a quantitative measure of the irregularly shaped morphologies and their underlying self-similar temporal behaviors. In this context, we explore the fractal nature of the gastrointestinal system and the potential of fractal geometry as a robust descriptor of its complex forms and functions. Additionally, we examine the practical applications of fractal geometry in clinical gastroenterology and hepatology practice.

This paper proposes an approach for the estimation of a time-varying Hurst exponent to allow accurate identification of multifractional Brownian motion (MFBM). The contribution provides a prescription for how to deal with the MFBM measurement data to solve regression and classification problems. Theoretical studies are supplemented with computer simulations and real-world examples. Those prove that the procedure proposed in this paper outperforms the best-in-class algorithm.

Irregularity in shape and behavior is the main feature of every anatomical system, including human organs, tissues, cells, and sub-cellular entities. It has been shown that this property cannot be quantified by means of the classical Euclidean geometry, which is only able to describe regular geometrical objects. In contrast, fractal geometry has been widely applied in several scientific fields. This rapid growth has also produced substantial insights in the biomedical imaging. Consequently, particular attention has been given to the identification of pathognomonic patterns of "shape" in anatomical entities and their changes from natural to pathological states. Despite the advantages of fractal mathematics and several studies demonstrating its applicability to oncological research, many researchers and clinicians remain unaware of its potential. Therefore, this review aims to summarize the complexity and fractal geometry of nuclear medicine images.

A hallmark of pancreatic ductal adenocarcinoma is the desmoplastic reaction, but its impact on the tumor behavior remains controversial. Our aim was to introduce a computer -aided method to precisely quantify the amount of pancreatic collagenic extra-cellular matrix, its spatial distribution pattern, and the degradation process.

A series of normal, inflammatory and neoplastic pancreatic ductal adenocarcinoma formalin-fixed and paraffin-embedded Sirius red stained sections were automatically digitized and analyzed using a computer-aided method.

We found a progressive increase of pancreatic collagenic extra-cellular matrix from normal to the inflammatory and pancreatic ductal adenocarcinoma. The two-dimensional fractal dimension showed a significant difference in the collagenic extra-cellular matrix spatial complexity between normal versus inflammatory and pancreatic ductal adenocarcinoma. A significant difference when comparing the number of cycles necessary to degrade the pancreatic collagenic extra-cellular matrix in normal versus inflammatory and pancreatic ductal adenocarcinoma was also found. The difference between inflammatory and pancreatic ductal adenocarcinoma was also significant. Furthermore, the mean velocity of collagenic extra-cellular matrix degradation was found to be faster in inflammatory and pancreatic ductal adenocarcinoma than in normal.

These findings demonstrate that inflammatory and pancreatic ductal adenocarcinomas are characterized by an increased amount of pancreatic collagenic extra-cellular matrix and by changes in their spatial complexity and degradation. Our study defines new features about the pancreatic collagenic extra-cellular matrix, and represents a basis for further investigations into the clinical behavior of pancreatic ductal adenocarcinoma and the development of therapeutic strategies.

Duchenne Muscular Dystrophy (DMD) is characterized by muscle extracellular matrix disorganization due to the increased collagen deposition leading to fibrosis that significantly exacerbates disease progression. Fractal dimension analysis is a method that quantifies tissue/cellular disorganization and characterizes complex structures. The first objective of the present study was use fractal analysis to evaluate extracellular matrix disorganization in mdx mice soleus muscle. Next, we mimic a hyper-proliferation of fibrogenic cells by co-culturing NIH3T3 fibroblasts and C2C12 myoblasts to test whether fibroblasts induce disorganization in myoblast arrangement. Here, we show mdx presented high skeletal muscle disorganization as revealed by fractal analysis. Similarly, this method revealed that myoblasts co-cultured with fibroblast also presented cellular arrangement disorganization. We also reanalyzed skeletal muscle microarrays transcriptomic data from mdx and DMD patients that revealed transcripts related to extracellular matrix organization. This analysis also identified Osteoglycin, which was validated as a potential regulator of ECM organization in mdx dystrophic muscles. Our results demonstrate that fractal dimension is useful tool for the analysis of skeletal muscle disorganization in DMD and also reveal a fibroblast-myoblast cross-talk that contributes to "in vitro" myoblast disarrangement.

This study was designed to establish whether the low volume and irregular border of the pancreas in type 2 diabetes would be normalised after reversal of diabetes.

A total of 29 individuals with type 2 diabetes undertook a very low energy (very low calorie) diet for 8 weeks followed by weight maintenance for 6 months. Methods were established to quantify the pancreas volume and degree of irregularity of the pancreas border. Three-dimensional volume-rendering and fractal dimension (FD) analysis of the MRI-acquired images were employed, as was three-point Dixon imaging to quantify the fat content.

There was no change in pancreas volume 6 months after reversal of diabetes compared with baseline (52.0 ± 4.9 cm(3) and 51.4 ± 4.5 cm(3), respectively; p = 0.69), nor was any volumetric change observed in the non-responders. There was an inverse relationship between the volume and fat content of the pancreas in the total study population (r =-0.50, p = 0.006). Reversal of diabetes was associated with an increase in irregularity of the pancreas borders between baseline and 8 weeks (FD 1.143 ± 0.013 and 1.169 ± 0.006, respectively; p = 0.05), followed by a decrease at 6 months (1.130 ± 0.012, p = 0.006). On the other hand, no changes in FD were seen in the non-reversed group.

Restoration of normal insulin secretion did not increase the subnormal pancreas volume over 6 months in the study population. A significant change in irregularity of the pancreas borders occurred after acute weight loss only after reversal of diabetes. Pancreas morphology in type 2 diabetes may be prognostically important, and its relationship to change in beta cell function requires further study.

Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes.

To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis.

Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05).

Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals.

The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.

Keratinocytes, in response to irritants, secrete pro-inflammatory mediators which recruit and activate immune and mesenchymal cells, including fibroblasts, to repair the skin. Fibroblasts respond by synthesising collagen and promoting the crosslinking extracellular matrix (ECM). We recently showed that the deletion of Rac1 in keratinocytes causes heightened inflammation due to aberrant crosstalk with immune cells. Indeed, the skin of these mice shows a higher inflammatory response to the induction of irritant contact dermatitis (ICD), and also even to treatment with a vehicle alone, compared with controls. As inflammation is intimately linked with fibrotic disease in the skin, this raised the question as to whether this deletion may also affect the deposition and arrangement of the dermal ECM. This study assessed the effects of Rac1 deletion in keratinocytes and of the heightened inflammatory status by induction of ICD on the tissue localisation and arrangements of dermal collagen. Qualitative analysis did not reveal evidence for the formation of pathologies in the dermis. However, quantitative analysis did reveal some perturbations in the dermal matrix, namely that only the combination of the lack of Rac1 and ICD affects the architectural organisation of the dermal collagen, and that a higher inflammatory state in the tissue (i.e. when Rac1 is deleted in the keratinocytes or ICD is induced in the skin, or a combination of both) influences the diameter of the collagen fibrils. It is proposed that this increase in the diameter of collagen fibrils due to inflammation may serve as pre-fibrotic marker enabling earlier determination of fibrosis and earlier treatment. This study has revealed previously unknown effects on the ECM due to the deletion of Rac1 in keratinocytes.

Apart from their effector functions in allergic disorders, tissue-resident mast cells (MC) are gaining recognition as initiators of inflammatory events through their distinctive ability to secrete many bioactive molecules harbored in cytoplasmic granules. Activation triggers mediator release through a regulated exocytosis named degranulation. MC activation is still substantiated by measuring systemic levels of MC-restricted mediators. However, identifying the anatomical location of MC activation is valuable for disease diagnosis. We designed a computer-assisted morphometric method based on image analysis of methylene blue (MB)-stained normal mouse skin tissue sections that quantitates actual in situ MC activation status. We reasoned MC cytoplasm could be viewed as an object featuring unique relative mass values based on activation status. Integrated optical density and area (A) ratios were significantly different between intact and degranulated MC (p<0.001). The examination of fractal characteristics is of translational diagnostic/prognostic value in cancer and readily applied to quantify cytoskeleton morphology and vasculature. Fractal dimension (D), a measure of their comparative space filling capacity and structural density, also differed significantly between intact and degranulated MC (p<0.001). Morphometric analysis provides a reliable and reproducible method for in situ quantification of MC activation status.

Endomyocardial biopsy to evaluate rejection in the transplanted heart is accepted at the "gold standard." The complexity of microscopic images suggested using digital methods for precise evaluating of acute rejection episodes with numerical representation. The aim of the present was study to characterize digitally acute rejection of the transplanted heart using complexity/fractal image analysis.

Biopsy samples harvested form 40 adult recipients after orthotropic heart transplantation were collected and rejection grade was evaluated according to the International Society for Heart and Lung Transplantation (0, 1a, 1b, or 3a) at transverse and longitudinal sections. Fifteen representative digital microscope images from each grade were collected and analyzed after Sobel edge detection and binarization.

Only mean fractal dimension showed a progressive and significant increase and correlation based on rejection grade using longitudinal sections. Lacunarity and number of foreground pixels showed unequivocal results.

Mean fractal diameter could serve as auxiliary digital parameter for grading of acute rejection in the transplanted heart.

Hearts of mice with reduction of function mutation in STAT3 (SA/SA) develop fibrotic collagen foci and reduced systolic function with hypertension. This model was used to determine if fractal dimension and image analysis can provide a quantitative description of myocardial fibrosis using routinely prepared trichome-stained material. Collagen was characterized by relative density [integrated optical density/area (IOD/A)] and fractal dimension (D), an index of complexity. IOD/A of collagen in wild type mice increased with hypertension while D decreased, suggesting tighter collagen packing that could eventually stiffen the myocardium as in diastolic heart failure. Reduced STAT3 function caused modest collagen fibrosis with increased IOD/A and D, indicating more tightly packed, but more disorganized collagen than normotensive and hypertensive controls. Hypertension in SA/SA mice resulted in large regions where myocytes were lost and replaced by fibrotic collagen characterized by decreased density and increased disorder. This indicates that collagen associated with reparative fibrosis in SA/SA hearts experiencing hypertension was highly disorganized and more space filling. Loss of myocytes and their replacement by disordered collagen fibers may further weaken the myocardium leading to systolic heart failure. Our findings highlight the utility of image analysis in revealing importance of a cellular protein for normal and reparative extracellular matrix deposition.

Hepatocellular carcinoma (HCC) remains a leading cause of death by cancer worldwide. Computerized diagnosis systems relying on novel imaging markers gained significant importance in recent years. Our aim was to integrate a novel morphometric measurement--the fractal dimension (FD)--into an artificial neural network (ANN) designed to diagnose HCC.

The study included 21 HCC and 28 liver metastases (LM) patients scheduled for surgery. We performed hematoxylin staining for cell nuclei and CD31/34 immunostaining for vascular elements. We captured digital images and used an in-house application to segment elements of interest; FDs were calculated and fed to an ANN which classified them as malignant or benign, further identifying HCC and LM cases.

User intervention corrected segmentation errors and fractal dimensions were calculated. ANNs correctly classified 947/1050 HCC images (90.2%), 1021/1050 normal tissue images (97.23%), 1215/1400 LM (86.78%), and 1372/1400 normal tissues (98%). We obtained excellent interobserver agreement between human operators and the system.

We successfully implemented FD as a morphometric marker in a decision system, an ensemble of ANNs designed to differentiate histological images of normal parenchyma from malignancy and classify HCCs and LMs.

The effects of aging on structural complexity in hematopoietic tissue are unknown. In this work, in a mouse experimental model, we report the age-related reduction of spleen hematopoietic tissue (SHT) complexity. Spleen tissue was obtained from the total of 64 male Swiss albino mice divided into 8 age groups: newborns (0 days old), 10 days, 20 days, 30 days, 120 days, 210 days, 300 and 390 days old. SHT was stained using conventional hematoxylin/eosin, and DNA-binding toluidine blue dyes. Fractal dimension as an indicator of cellular complexity, and lacunarity as indicator of tissue heterogeneity were determined based on the binarized SHT micrographs. Results indicate that fractal dimension of mice spleen hematopoietic tissue decreases with age, while lacunarity increases. These changes/trends have been detected in SHT stained both with toluidine blue and conventional hematoxylin/eosin. Fractal dimension was negatively correlated with lacunarity. The detected reduction in complexity suggests that age-related structural changes are present in mouse SHT both in general tissue architecture and progenitor cell DNA.

Recent studies have shown that ghrelin increases pancreatic exocrine secretion. However, the potential effects of ghrelin on the morphology of exocrine pancreas (EP) remain unknown. In this work, using fractal analysis, we demonstrate that centrally administered ghrelin increases structural complexity and tissue disorder in rat EP. The study was carried out on a total of 40 male Wistar rats divided into four groups (n = 10): ghrelin-treated animals (average age, 1.5 months), ghrelin-treated animals (8.5 months), and controls (1.5 and 8.5 months). The pancreas tissue sections were stained with hematoxylin/eosin and visualized by light microscopy. For each animal, the average values of tissue fractal dimension, lacunarity, as well as parameters of co-occurrence matrix texture, were determined using tissue digital micrographs. The results indicate that ghrelin administration increases EP fractal dimension and textural entropy, and decreases lacunarity, regardless of the age. To our knowledge, this is the first study to investigate the effects of ghrelin on the morphological properties of pancreatic tissue, and also the first to apply fractal and textural analysis methods in quantification of EP tissue architecture.

Tocotrienols exhibit anti-inflammatory properties over macrophages and promote cytotoxicity in activated pancreatic stellate cells, suggesting that they may limit chronic pancreatitis progression. We aimed to quantitate the effect of oral tocotrienols on a rat model of chronic pancreatic injury. Chronic-like pancreatitis was induced by repeated arginine pancreatitis. Palm oil tocotrienol-rich fraction (TRF) was given by gavage before and after pancreatitis inductions. Amylase and hydroxyproline were determined in pancreatic homogenates; collagen, fibronectin, α-smooth muscle actin (SMA), glial fibrillary acidic protein (GFAP), and phosphorylated Smad3 were assessed by Western blotting. Transforming growth factor (TGF)-β1 was measured in plasma. Morphological assessment included light microscopy, fibrosis area fraction, and collagen network fractal analysis. Arginine pancreatitis induced pancreatic atrophy and increased hydroxyproline that ameliorated after TRF. Arginine increased TGF-β1 (185 ± 40 vs. 15 ± 2 ng/ml; P <0.01) that was blunted by TRF (53 ± 19; P < 0.01). TRF reduced protease and Smad3 activation, collagen, and fibronectin. α-SMA increased and GFAP diminished in arginine pancreatitis, consistent with long-term stellate cell activation, and TRF reverted these changes to basal. Arginine pancreatitis increased fibrosis area fraction (4.5 ± 0.3% vs. 0.2 ± 0.2%), collagen network complexity (fractal dimension 1.52 ± 0.03 vs. 1.42 ± 0.01; P < 0.001), and inhomogeneity (lacunarity 0.63 ± 0.03 vs. 0.40 ± 0.02; P < 0.001), which were all reduced by TRF (1.3 ± 0.4%, 1.43 ± 0.02%, and 0.51 ± 0.03%, respectively; P < 0.01). Best correlation coefficients were obtained when comparing fibrosis area fraction with lacunarity (r = 0.88) and both parameters with pancreatic weight (r = -0.91 and -0.79, respectively). TRF administered only before pancreatitis best, but not fully, recapitulated the beneficial effects of TRF. Tocotrienols improve quantitative measures of chronic pancreatic damage. They may be of benefit in human chronic pancreatitis.

To describe a quantitative analysis method for liver biopsy sections with a machine that we have named "Dioguardi Histological Metriser" which automatically measures the residual hepatocyte mass (including hepatocytes vacuolization), inflammation, fibrosis and the loss of liver tissue tectonics.

We analysed digitised images of liver biopsy sections taken from 398 patients. The analysis with Dioguardi Histological Metriser was validated by comparison with semi-quantitative scoring system.

The method provides: (1) the metrical extension in two-dimensions (the plane) of the residual hepatocellular set, including the area of vacuoles pertinent to abnormal lipid accumulation; (2) the geometric measure of the inflammation basin, which distinguishes intra-basin space and extra-basin dispersed parenchymal leukocytes; (3) the magnitude of collagen islets, (which were considered truncated fractals and classified into three degrees of magnitude); and (4) the tectonic index that quantifies alterations (disorders) in the organization of liver tissue. Dioguardi Histological Metriser machine allows to work at a speed of 0.1 mm(2)/s, scanning a whole section in 6-8 min.

The results are the first standardized metrical evaluation of the geometric properties of the parenchyma, inflammation, fibrosis, and alterations in liver tissue tectonics of the biopsy sections. The present study confirms that biopsies are still valuable, not only for diagnosing chronic hepatitis, but also for quantifying changes in the organization and order of liver tissue structure.

Liver fibrosis is a common pathway leading to cirrhosis, which is the final result of injury to the liver. Accurate assessment of the degree of fibrosis is important clinically, especially when treatments aimed at reversing fibrosis are being evolved. Liver biopsy has been considered to be the "gold standard" to assess fibrosis. However, liver biopsy being invasive and, in many instances, not favored by patients or physicians, alternative approaches to assess liver fibrosis have assumed great importance. Moreover, therapies aimed at reversing the liver fibrosis have also been tried lately with variable results. Till now, there has been no consensus on various clinical, pathological, and radiological aspects of liver fibrosis. The Asian Pacific Association for the Study of the Liver set up a working party on liver fibrosis in 2007, with a mandate to develop consensus guidelines on various aspects of liver fibrosis relevant to disease patterns and clinical practice in the Asia-Pacific region. The process for the development of these consensus guidelines involved the following: review of all available published literature by a core group of experts; proposal of consensus statements by the experts; discussion of the contentious issues; and unanimous approval of the consensus statements after discussion. The Oxford System of evidence-based approach was adopted for developing the consensus statements using the level of evidence from 1 (highest) to 5 (lowest) and grade of recommendation from A (strongest) to D (weakest). The consensus statements are presented in this review.

Hepatitis C virus (HCV) is still one of the major causes of chronic viral infection worldwide, and hepatic steatosis is a frequent pathological finding in patients with chronic HCV-related diseases. It is unclear whether the steatosis is associated with host factors or the virus itself, although a consistent relationship has been found between steatosis and a necro-inflammatory reaction with the increased secretion of immuno-regulators. A primary sources of inflammatory mediators are mast cells (MCs) bone marrow-derived cells that are detected in both normal and diseased livers. We determined MC density and correlated it with the fibrosis, inflammatory reaction and steatosis observed in the liver biopsies of patients affected by HCV with or without steatosis. All the histological features were assessed using a computer-aided image analysis system. There was a statistically significant difference in MC density between the HCV-infected patients with and without steatosis, with the lower mean value being detected in those without (P < 0.02). Furthermore, a nonstatistically significant difference in fibrosis and inflammation between the two patient groups was found. In conclusion, this is the first study showing a significant increase in MC density in the tissues of patients with chronic HCV infection and histologically documented steatosis.

To assess the sampling variability of computer-aided, fractal-corrected measures of fibrosis in liver biopsies.

Samples were derived from six to eight different parts of livers removed from 12 patients with clinically and histologically proven cirrhosis undergoing orthotopic liver transplantation. Sirius red-stained sections with a thickness of 2 mum were digitized using a computer-aided image analysis system that automatically measures the surface of fibrosis, as well as its outline perimeter, fractal surface and outline dimensions, wrinkledness, and Hurst coefficient.

We found a high degree of inter-sample variability in the measurements of the surface [coefficient of variation (CV) = 43% +/- 13%] and wrinkledness (CV = 28% +/- 9%) of fibrosis, but the inter-sample variability of Hurst's exponent was low (CV = 14% +/- 2%).

This study suggests that Hurst's exponent might be used in clinical practice as the best histological estimate of fibrosis in the whole organ, and evidences the fact that biopsy sections, which are fundamental for the qualitative diagnosis of chronic hepatitis, play a key role in the quantitative estimate of architectural changes in liver tissue.