Self-organization of developing embryo using scale-invariant approach

Novel Fractal-Based Sub-RPE Compartment OCT Radiomics Biomarkers Are Associated With Subfoveal Geographic Atrophy in Dry AMD

OBJECTIVE

The purpose of this study was to quantitatively characterize the shape of the sub-retinal pigment epithelium (sub-RPE, i.e., space bounded by RPE and Bruch's membrane) compartment on SD-OCT using fractal dimension (FD) features and evaluate their impact on risk of subfoveal geographic atrophy (sfGA) progression.

METHODS

This was an IRB-approved retrospective study of 137 subjects with dry age-related macular degeneration (AMD) with subfoveal GA. Based on sfGA status at year five, eyes were categorized as "Progressors" and "Non-progressors". FD analysis allows quantification of the degree of shape complexity and architectural disorder associated with a structure. To characterize the structural irregularities along the sub-RPE surface between the two groups of patients, a total of 15 shape descriptors of FD were extracted from the sub-RPE compartment of baseline OCT scans. The top four features were identified using minimum Redundancy maximum Relevance (mRmR) feature selection method and evaluated with Random Forest (RF) classifier using three-fold cross validation from the training set (N = 90). Classifier performance was subsequently validated on the independent test set (N = 47).

RESULTS

Using the top four FD features, a RF classifier yielded an AUC of 0.85 on the independent test set. Mean fractal entropy (p-value = 4.8e-05) was identified as the most significant biomarker; higher values of entropy being associated with greater shape disorder and risk for sfGA progression.

CONCLUSIONS

FD assessment holds promise for identifying high-risk eyes for GA progression.

SIGNIFICANCE

With further validation, FD features could be potentially used for clinical trial enrichment and assessments for therapeutic response in dry AMD patients.

Data-Theoretical Synthesis of the Early Developmental Process

Biological development is often described as a dynamic, emergent process. This is evident across a variety of phenomena, from the temporal organization of cell types in the embryo to compounding trends that affect large-scale differentiation. To better understand this, we propose combining quantitative investigations of biological development with theory-building techniques. This provides an alternative to the gene-centric view of development: namely, the view that developmental genes and their expression determine the complexity of the developmental phenotype. Using the model system Caenorhabditis elegans, we examine time-dependent properties of the embryonic phenotype and utilize the unique life-history properties to demonstrate how these emergent properties can be linked together by data analysis and theory-building. We also focus on embryogenetic differentiation processes, and how terminally-differentiated cells contribute to structure and function of the adult phenotype. Examining embryogenetic dynamics from 200 to 400 min post-fertilization provides basic quantitative information on developmental tempo and process. To summarize, theory construction techniques are summarized and proposed as a way to rigorously interpret our data. Our proposed approach to a formal data representation that can provide critical links across life-history, anatomy and function.

Adaptive self-organization in the embryo: its importance to adult anatomy and to tissue engineering

The anatomy of healthy humans shows much minor variation, and twin‐studies reveal at least some of this variation cannot be explained genetically. A plausible explanation is that fine‐scale anatomy is not specified directly in a genetic programme, but emerges from self‐organizing behaviours of cells that, for example, place a new capillary where it happens to be needed to prevent local hypoxia. Self‐organizing behaviour can be identified by manipulating growing tissues (e.g. putting them under a spatial constraint) and observing an adaptive change that conserves the character of the normal tissue while altering its precise anatomy. Self‐organization can be practically useful in tissue engineering but it is limited; generally, it is good for producing realistic small‐scale anatomy but large‐scale features will be missing. This is because self‐organizing organoids miss critical symmetry‐breaking influences present in the embryo: simulating these artificially, for example, with local signal sources, makes anatomy realistic even at large scales. A growing understanding of the mechanisms of self‐organization is now allowing synthetic biologists to take their first tentative steps towards constructing artificial multicellular systems that spontaneously organize themselves into patterns, which may soon be extended into three‐dimensional shapes.

Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos

Embryonic development proceeds through a series of differentiation events. The mosaic version of this process (binary cell divisions) can be analyzed by comparing early development of Ciona intestinalis and Caenorhabditis elegans. To do this, we reorganize lineage trees into differentiation trees using the graph theory ordering of relative cell volume. Lineage and differentiation trees provide us with means to classify each cell using binary codes. Extracting data characterizing lineage tree position, cell volume, and nucleus position for each cell during early embryogenesis, we conduct several statistical analyses, both within and between taxa. We compare both cell volume distributions and cell volume across developmental time within and between single species and assess differences between lineage tree and differentiation tree orderings. This enhances our understanding of the differentiation events in a model of pure mosaic embryogenesis and its relationship to evolutionary conservation. We also contribute several new techniques for assessing both differences between lineage trees and differentiation trees, and differences between differentiation trees of different species. The results suggest that at the level of differentiation trees, there are broad similarities between distantly related mosaic embryos that might be essential to understanding evolutionary change and phylogeny reconstruction. Differentiation trees may therefore provide a basis for an Evo-Devo Postmodern Synthesis.

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

The role of self-organization in developmental evolution

In developmental and evolutionary biology, particular emphasis has been given to the relationship between transcription factors and the cognate cis-regulatory elements of their target genes. These constitute the gene regulatory networks that control expression and are assumed to causally determine the formation of structures and body plans. Comparative analysis has, however, established a broad sequence homology among species that nonetheless display quite different anatomies. Transgenic experiments have also confirmed that many developmentally important elements are, in fact, functionally interchangeable. Although dependent upon the appropriate degree of gene expression, the actual construction of specific structures appears not directly linked to the functions of gene products alone. Instead, the self-formation of complex patterns, due in large part to epigenetic and non-genetic determinants, remains a persisting theme in the study of ontogeny and regenerative medicine. Recent evidence indeed points to the existence of a self-organizing process, operating through a set of intrinsic rules and forces, which imposes coordination and a holistic order upon cells and tissue. This has been repeatedly demonstrated in experiments on regeneration as well as in the autonomous formation of structures in vitro. The process cannot be wholly attributed to the functional outcome of protein-protein interactions or to concentration gradients of diffusible chemicals. This phenomenon is examined here along with some of the methodological and theoretical approaches that are now used in understanding the causal basis for self-organization in development and its evolution.

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed.