Microstructural characterization of chitosan and alginate films by microscopy techniques and texture image analysis

The aim of this work is to characterize the microstructure of chitosan and alginate edible films by microscopy techniques and texture image analysis. Edible films were obtained by solution casting and solvent evaporation. The microscopy techniques used in this work were: light, environmental scanning electron and atomic force microscopy. Textural features and fractal dimension were extracted from the images. Entropy and fractal dimension were more useful to evaluate the complexity and roughness of films. The highest values of entropy and fractal dimension corresponded to alginate/chitosan, followed of alginate and chitosan films. An entropy/fractal dimension ratio, proposed here, was useful to characterize the degree of image complexity and roughness of edible films at different magnifications. It was possible to postulate that microscopy techniques combined with texture image analysis are efficient tools to quantitatively evaluate the surface morphology of edible films made of chitosan and alginate.     

Is the complexity of the human sagittal suture related to the size of the temporal muscle?

We have tested the hypothesis that temporal muscle size determines the degree of interdigitation of the human sagittal suture by comparing male and female skulls of Europeans and Australian aborigines. Temporal muscle length, area of the temporal aperture and estimated muscle volume were greater in males than in females of each racial group. Sexual dimorphism of the complexity of the sagittal suture was not confirmed in either race. However, the suture was less complex in aborigines than Europeans despite the volume of the temporal muscle being larger in the former group. We conclude, therefore, that although the morphology of the sagittal suture is an epigenetic character, it is not mechanically influenced by muscle size. A simple quantitation of suture form may however be useful in assigning unknown skulls to a particular race.     

Cranial Suture Morphology and its Relationship to Diet in Cebus

Cranial sutures are complex morphological structures. Four Cebus species (C. albifrons, C. apella, C. capucinus, C. olivaceus) are used here to test the hypothesis that sagittal suture complexity is enhanced in animals that eat materially challenging foods. These primates are ideal for such comparative studies because they are closely related and some are known to exhibit differences in the material properties of the foods they ingest and masticate. Specifically, Cebus apella is notable among members of this genus for ingesting food items of high toughness as well as consistently demonstrating a relatively robust cranial morphology. Consistent with previous studies, C. apella demonstrates significantly more robust mandibular and temporal fossa morphology. Also, C. apella possesses sagittal sutures that are more complex than congenerics. These data are used to support the hypothesis that cranial suture complexity is increased in response to consuming diets with more obdurate material properties. One interpretation of this hypothesis is that, compared to non-apelloids, total strain in the apelloid cranial suture connective tissue environment is elevated due to increased jaw muscle activity by increases in either force magnitudes or the number of chewing events. It is argued that greater masticatory function enhances the growth and modeling of cranial suture interdigitation. These data show that cranial suture complexity is one more hard tissue feature from the skull that might be used to inform hypotheses of dietary functional morphology.     

Analysis of fractal dimension of O2A glial cells differentiating in vitro

Fractal dimension is a quantitative measure of morphological complexity. Glial cells of the oligodendrocyte-type 2 astrocyte (O2A) lineage exhibit increasing morphological complexity as they differentiate in vitro. Enriched populations of O2A progenitor cells isolated from neonatal rat cerebral hemispheres or optic nerves were allowed to differentiate in vitro, and their fractal dimensions were measured over time. The fractal dimensions of the maturing cells correlated with perceived complexity; cells with elaborate process branching had larger fractal dimensions than cells with a simpler morphology. An analysis of changes in fractal dimension revealed distinct rates of growth for both oligodendrocytes and type 2 astrocytes. The fractal dimension remained constant over a 10-fold range in optical magnification, demonstrating that cultured O2A glial cells exhibit self-similarity, a defining characteristic of fractal objects. These results illustrate that fractal dimension analysis of maturing cell populations is a useful method for quantitatively describing the process of cell differentiation.     

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean D_b = 1.45) with respect to their 2‐D coiled counterparts (mean D_b = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.     

Fractal analysis of the Orce skull sutures

Methods of fractal geometry (Mandelbrot, 1983) are used here to analyse the relative complexity of the sagittal and lambdoid sutures visible in the skull fragment formed by parts of an occipital squame and parietals found in a sealed deposit at the early Lower Pleistocene site of Venta Micena (Orce, Granada, Spain), generally regarded as human bone but occasionally suggested as belonging to an equid. For comparison with the fossil, corresponding sutures of various primates (hominids, pongids and cercopithecids) and two other groups of mammals (equids and ruminants) were analysed using the computer program FRACTAL-D (Slice, 1989) in order to determine their fractal dimensions as a measure of differential sutural design complexity. The results show that the fractal dimension of the Venta Micena skull sutures lies within the range of variation for infant specimens of both modern and Plio-Pleistocene hominids. Sutural complexity in young pongids and cercopithecids overlaps the range of fractal dimensions found in hominids, whereas values obtained from equids and ruminants are significantly greater than those for all the primates analysed here. Therefore, in terms of fractal dimension measures of relative complexity, the sutures preserved in the Venta Micena fossil could not have belonged to an equid (pace Agusti & Moyà-Sola, 1987); rather, its fractal dimension is consistent with the attribution of the fossil to an infant of Homo sp.     

Fractal morphometry of cell complexity.

Irregularity and self-similarity under scale changes are the main attributes of the morphological complexity of both normal and abnormal cells and tissues. In other words, the shape of a self-similar object does not change when the scale of measurement changes, because each part of it looks similar to the original object. However, the size and geometrical parameters of an irregular object do differ when it is examined at increasing resolution, which reveals more details. Significant progress has been made over the past three decades in understanding how irregular shapes and structures in the physical and biological sciences can be analysed. Dominant influences have been the discovery of a new practical geometry of Nature, now known as fractal geometry, and the continuous improvements in computation capabilities. Unlike conventional Euclidean geometry, which was developed to describe regular and ideal geometrical shapes which are practically unknown in nature, fractal geometry can be used to measure the fractal dimension, contour length, surface area and other dimension parameters of almost all irregular and complex biological tissues. We have used selected examples to illustrate the application of the fractal principle to measuring irregular and complex membrane ultrastructures of cells at specific functional and pathological stage.     

红树植物木榄幼树斑块形状的分形分析

应用分形理论分析了山口国家级红树林自然保护区木榄幼树斑块形状的分形特征。木榄幼树斑块在整体水平上的分形维数为 1 .1 2 ,而单个斑块的分形维数介于 1 .1 7～ 1 .3 7之间。分形维数的大小与斑块形状的复杂程度密切相关。频谱法和周长 -面积法都适用于分析幼树斑块形状的分形特征。     

Fractal analysis and its applications in human palaentology

Fractal analysis was applied in human palaentology by Gibert and Palmqvist to estimate the value of the fractal dimension obtained from the cranial sutures preserved in the fragment of occipital bone (VM-0) found at the Venta Micena site. This paper also estimated the values of fractal dimension for different specimens in order to establish a taxonomy. Although that initial study demonstrated that the technique could be useful in human palaentology, the large variability of sutures observed in the VM-0 sample requires a mechanism that makes it possible to automatically obtain an objective plot of the suture to be analyzed.     

Finger-like lysing patterns of blood clots.

One-dimensional modeling of fibrinolysis (Senf, 1979; Zidansek and Blinc, 1991; Diamond and Anand, 1993) has accounted for the dissolution velocity, but the shape of the lysing patterns can be explained only by two- or three- drug-induced blood clot dissolution patterns obtained by proton nuclear magnetic resonance imaging, which can be described by the enzyme transport-limited system of fibrinolytic chemical equations with diffusion and perfusion terms (Zidansek and Blinc, 1991) in the reaction time approximation if the random character of gel porosity is taken into account. A two-dimensional calculation based on the Hele-Shaw random walk models (Kadanoff, 1985; Liang, 1986) leads to fractal lysing patterns as, indeed, is observed. The fractal dimension of the experimental lysing patterns changes from 1.2 at the beginning of the experiments to a maximum of approximately 1.3 in the middle and then decreases toward one when the clot is recanalized.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

Visual discrimination of fractal borders.

The ideas of fractals and fractal dimension are here translated into the realm of visual psychophysics. Borders between two fields of different luminance were used. Because of the finite grain of the visual system, fractal dimension need be defined only within a certain size range. For a fractal dimension of 1.15, the just-detectable difference in fractal dimension was found to be about 0.0085, rising to about 0.015 for a fractal dimension of 1.25. Reducing exposure duration from 1 s to 0.33 s decreases sensitivity to differences in fractal dimension, but there was no gain in increasing the exposure duration. Good visual observers who are naive to the task require some training before reaching optimal performance. The ability to discriminate fractal dimension differs between fractal edges of the same fractal dimension that were generated with differing statistical programs. Even after considerable training, an observer makes 29% errors when asked to distinguish a fractal edge generated with a Gaussian random walk from one with a rectangular random walk. Gaussian random walk fractals can be more easily distinguished from Poissonian and Cauchy ones.     

Effects of macrophyte architecture and leaf shape complexity on structural parameters of the epiphytic algal community in a Pampean stream

Habitat heterogeneity is one of the main factors determining distribution of organisms, and vegetation is of primary importance in shaping the structural environment in aquatic systems. The effect of macrophyte complexity on macroinvertebrates has been well researched; however, much remains to be revealed about the influence of complexity on epiphytic algae. Here, we used fractal dimension to study the effect of complexity at two scales, macrophyte architecture and leaf shape, on several parameters of the epiphytic algal community (number of individuals, biomass, taxon richness and diversity) in a Pampean stream. Four submerged macrophyte species with different complexities and associated algae were sampled in late spring, summer and autumn. Important differences were found in fractal dimension of the whole plant and leaves among macrophyte species. The particulate organic matter and chlorophyll a associated positively to leaf fractal dimension, but not to plant fractal dimension, partially supporting the hypothesis of a positive effect of macrophyte complexity on periphyton biomass. No association was found in fractal dimension with algal abundance, taxon richness or diversity. Complementary, a mesocosm experiment was performed with plastic imitations of different plant fractal dimensions. After four weeks, there were differences in chlorophyll a and autotrophy index between treatments that suggested a positive effect of complexity on autotrophic periphyton biomass. These results indicate that the well-known positive effect of macrophyte complexity on macroinvertebrates might be partially explained by a positive effect of complexity on periphyton biomass.     

Cranial suture complexity in white-tailed deer (Odocoileus virginianus)

Neurocranial expansion and mastication are commonly implicated as the two major biomechanical factors affecting suture morphology. In deer the antlers provide an additional source of biomechanical stress acting on the skull. Equivalent stresses are not found in females, who lack antlers. We analyzed the complexity and interdigitation of the interfrontal and coronal sutures that surround the antler-bearing frontal bones of (n = 67) white-tailed deer (Odocoileus virginianus) to 1) evaluate changes in suture morphology throughout ontogeny, and 2) test the hypothesis that male deer have more complex sutures than females. Two methods were used to quantify suture morphology: fractal analysis and length-ratios (actual suture length divided by direct straightline length). Both techniques produced similar results, although the two methods cannot be considered equivalent. Suture complexity increases markedly throughout ontogeny, but appears to level off after animals have reached adulthood. Cranial size in males, but not females, continues to increase in adults. No significant increase in suture complexity with age in the adult cohort was detected. While deer are highly dimorphic in size and the presence of antlers, no significant differences existed between males and females for any measure of suture complexity. No consistent patterns emerged between suture complexity and skull size or antler characteristics. The presence of antlers appears to have a minimal effect on suture complexity in white-tailed deer. Factors that may contribute to the lack of dimorphism in suture complexity are discussed.     

The effects of morphological irregularity on the mechanical behavior of interdigitated biological sutures under tension

Irregular interdigitated morphology is prevalent in biological sutures in nature. Suture complexity index has long been recognized as the most important morphological parameter to govern the mechanical properties of biological sutures. However, the suture complexity index alone does not reflect all aspects of suture morphology. The goal of this investigation was to determine that besides suture complexity index, whether the degree of morphological irregularity of biological sutures has influences on the mechanical properties, and if there is any, how to quantify these influences. To explore these issues, theoretical and finite element (FE) suture models with the same suture complexity index but different levels of morphological irregularity were developed. The quasi-static stiffness, strength for damage initiation and post-failure process of irregular sutures were studied. It was shown that for the same suture complexity index, when the level of morphological irregularity increases, the overall strain to failure will increase while tensile stiffness is retained; also, the total energy to fracture increases with a sacrifice in strength to damage initiation. These results reveal that morphological irregularity is another important independent parameter to govern and balance the mechanical properties of biological sutures. Therefore, from the mechanics point of view, the prevalence of irregular suture morphology in nature is a merit, not a defect.     

Endoscopic craniectomy for early correction of craniosynostosis

Twelve patients between 0.4 and 7.8 months of age were treated by an endoscopic approach to strip craniectomy. Nine patients had sagittal suture involvement. Two patients had a single unilateral lambdoid suture synostosis, and one patient had a combination of a right coronal synostosis and a metopic synostosis. Postoperatively, all patients were placed in cranial remodeling helmets and the results showed that the estimated blood loss ranged from 5 cc to 150 cc, with blood transfusion required in only one patient. All patients were discharged from the hospital by day 2, and all patients had an improvement in their cranial head shape. The specific technique of using the endoscope to aid in performing a strip craniectomy will be discussed. Nine endoscopically treated patients with the diagnosis of sagittal suture synostosis were compared with nine patients treated by using the Marchac remodeling techniques. The mean operative time (1.6 hours versus 3.5 hours), estimated blood loss (43 cc versus 168 cc), hospital costs ($11,671 versus $36,685), and length of stay (1.16 days versus 5.1 days) were less by using the endoscopic technique. All nine patients treated by using the Marchac technique required a blood transfusion, whereas only one patient was transfused in the endoscopically treated group.     

Fractal landscapes and molecular evolution: modeling the myosin heavy chain gene family.

Mapping nucleotide sequences onto a "DNA walk" produces a novel representation of DNA that can then be studied quantitatively using techniques derived from fractal landscape analysis. We used this method to analyze 11 complete genomic and cDNA myosin heavy chain (MHC) sequences belonging to 8 different species. Our analysis suggests an increase in fractal complexity for MHC genes with evolution with vertebrate > invertebrate > yeast. The increase in complexity is measured by the presence of long-range power-law correlations, which are quantified by the scaling exponent alpha. We develop a simple iterative model, based on known properties of polymeric sequences, that generates long-range nucleotide correlations from an initially noncorrelated coding region. This new model-as well as the DNA walk analysis-both support the intron-late theory of gene evolution.