Complexity, fractals, disease time, and cancer

Fractal Changes of the Retinal Microvasculature in Syphilitic Uveitis

PURPOSE

To quantify chorioretinal microvascular damage and recovery post-treatment in patients with acute syphilitic posterior placoid chorioretinitis (ASPPC) using fractal dimension (FD).

METHODS

Retrospective cohort study of patients with serologically confirmed syphilitic uveitis. We obtained optical coherence tomography angiography (OCTA) scans at baseline and follow-up after intravenous penicillin treatment and computed FD of the superficial capillary plexus (SCP), deep capillary plexus (DCP), and choriocapillaris (CC) using ImageJ.

RESULTS

We enrolled seven patients with ASPPC (11 eyes), and 17 control subjects (34 eyes). Pre-treatment averages of FD-SCP, FD-DCP, and FD-CC were: 1.672 (±0.115), 1.638 (±0.097), and 1.72 (±0.137); post-treatment: 1.760 (±0.071), 1.764 (±0.043), and 1.898 (±0.047). After treatment FD-CC increased in all 11 eyes with an average of 0.163 (p = 0.003); FD-DCP increased in 10 (91%) eyes with an average of 0.126 (p = 0.003); and FD-SCP increased in seven (64%) eyes with an average of 0.089 (p = 0.059). Compared to the post-treatment FD values in the syphilitic group, controls had similar FD-SCP (p = 0.266), FD-DCP (p = 0.078), and FD-CC (p = 0.449).

CONCLUSIONS

CC and DCP are mostly affected in ASPPC with minimal changes in the SCP. All vascular layers FD recovered after completing antibiotic treatment.

Fractal Analysis in Clinical Neurosciences: An Overview

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

An Emergence Framework of Carcinogenesis

Experimental paradigms provide the framework for the understanding of cancer, and drive research and treatment, but are rarely considered by clinicians. The somatic mutation theory (SMT), in which cancer is considered a genetic disease, has been the predominant traditional model of cancer for over 50 years. More recently, alternative theories have been proposed, such as tissue organization field theory (TOFT), evolutionary models, and inflammatory models. Key concepts within the various models have led to them being difficult to reconcile. Progressively, it has been recognized that biological systems cannot be fully explained by the physicochemical properties of their constituent parts. There is an increasing call for a 'systems' approach. Incorporating the concepts of 'emergence', 'systems', 'thermodynamics', and 'chaos', a single integrated framework for carcinogenesis has been developed, enabling existing theories to become compatible as alternative mechanisms, facilitating the integration of bioinformatics and providing a structure in which translational research can flow from both 'benchtop to bedside' and 'bedside to benchtop'. In this review, a basic understanding of the key concepts of 'emergence', 'systems', 'system levels', 'complexity', 'thermodynamics', 'entropy', 'chaos', and 'fractals' is provided. Non-linear mathematical equations are included where possible to demonstrate compatibility with bioinformatics. Twelve principles that define the 'emergence framework of carcinogenesis' are developed, with principles 1-10 encapsulating the key concepts upon which the framework is built and their application to carcinogenesis. Principle 11 relates the framework to cancer progression. Principle 12 relates to the application of the framework to translational research. The 'emergence framework of carcinogenesis' collates current paradigms, concepts, and evidence around carcinogenesis into a single framework that incorporates previously incompatible viewpoints and ideas. Any researcher, scientist, or clinician involved in research, treatment, or prevention of cancer can employ this framework.

Tumor proliferation and diffusion on percolation clusters

We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.

Phase transitions in pancreatic islet cellular networks and implications for type-1 diabetes

In many aspects the onset of a chronic disease resembles a phase transition in a complex dynamic system: Quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we examine a special case, the onset of type-1 diabetes (T1D), a disease that results from loss of the insulin-producing pancreatic islet β cells. Within each islet, the β cells are electrically coupled to each other via gap-junctional channels. This intercellular coupling enables the β cells to synchronize their insulin release, thereby generating the multiscale temporal rhythms in blood insulin that are critical to maintaining blood glucose homeostasis. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity. In particular, the critical amount of β-cell death at which the islet cellular network loses site percolation is consistent with laboratory and clinical observations of the threshold loss of β cells that causes islet functional failure. In addition, numerical simulations confirm that the islet cellular network needs to be percolated for β cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after onset of T1D and introduction of treatment, potentially explaining the honeymoon phenomenon. Based on these results, we hypothesize that the onset of T1D may be the result of a phase transition of the islet β-cell network.

Unifying complexity and information

Complex systems, arising in many contexts in the computer, life, social, and physical sciences, have not shared a generally-accepted complexity measure playing a fundamental role as the Shannon entropy H in statistical mechanics. Superficially-conflicting criteria of complexity measurement, i.e. complexity-randomness (C-R) relations, have given rise to a special measure intrinsically adaptable to more than one criterion. However, deep causes of the conflict and the adaptability are not much clear. Here I trace the root of each representative or adaptable measure to its particular universal data-generating or -regenerating model (UDGM or UDRM). A representative measure for deterministic dynamical systems is found as a counterpart of the H for random process, clearly redefining the boundary of different criteria. And a specific UDRM achieving the intrinsic adaptability enables a general information measure that ultimately solves all major disputes. This work encourages a single framework coving deterministic systems, statistical mechanics and real-world living organisms.

In vivo quantitative microvasculature phenotype imaging of healthy and malignant tissues using a fiber-optic confocal laser microprobe

Real-time in vivo imaging of the microvasculature may help both earlier clinical detection of disease and the understanding of tumor-host interaction at various stages of progression. In vivo confocal and multiphoton microscopy is often hampered by bulky optics setup and has limited access to internal organs. A fiber-optic setup avoids these limitations and offers great user maneuverability. We report here the in vivo validation of a fiber-optic confocal fluorescence microprobe imaging system. In addition, we developed an automated fractal-based image analysis to characterize microvascular morphology based on vessel diameter distribution, density, volume fraction, and fractal dimension from real-time data. The system is optimized for use in the far-red and near-infrared region. The flexible 1.5-mm-diameter fiber-optic bundle and microprobe enable great user maneuverability, with a field of view of 423 x 423 microm and a tissue penetration of up to 15 microm. Lateral and axial resolutions are 3.5 and 15 microm. We show that it is possible to obtain high temporal and spatial resolution images of virtually any abdominal viscera in situ using a far-red blood pool imaging probe. Using an orthotopic model of pancreatic ductal adenocarcinoma, we characterized the tumor surface capillary and demonstrated that the imaging system and analysis can quantitatively differentiate between the normal and tumor surface capillary. This clinically approved fiber-optic system, together with the fractal-based image analysis, can potentially be applied to characterize other tumors in vivo and may be a valuable tool to facilitate their clinical evaluation.

Fractal analysis in a systems biology approach to cancer

Cancer is a highly complex disease due to the disruption of tissue architecture. Thus, tissues, and not individual cells, are the proper level of observation for the study of carcinogenesis. This paradigm shift from a reductionist approach to a systems biology approach is long overdue. Indeed, cell phenotypes are emergent modes arising through collective non-linear interactions among different cellular and microenvironmental components, generally described by "phase space diagrams", where stable states (attractors) are embedded into a landscape model. Within this framework, cell states and cell transitions are generally conceived as mainly specified by gene-regulatory networks. However, the system's dynamics is not reducible to the integrated functioning of the genome-proteome network alone; the epithelia-stroma interacting system must be taken into consideration in order to give a more comprehensive picture. Given that cell shape represents the spatial geometric configuration acquired as a result of the integrated set of cellular and environmental cues, we posit that fractal-shape parameters represent "omics" descriptors of the epithelium-stroma system. Within this framework, function appears to follow form, and not the other way around.

A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics

Cancer begins to be recognized as a highly complex disease, and advanced knowledge of the carcinogenic process claims to be acquired by means of supragenomic strategies. Experimental data evidence that tumor emerges from disruption of tissue architecture, and it is therefore consequential that the tissue level should be considered the proper level of observation for carcinogenic studies. This paradigm shift imposes to move from a reductionistic to a systems biology approach. Indeed, cell phenotypes are emergent modes arising through collective nonlinear interactions among different cellular and microenvironmental components, generally described by a phase space diagram, where stable states (attractors) are embedded into a landscape model. Within this framework cell states and cell transitions are generally conceived as mainly specified by the gene-regulatory network. However, the system's dynamics cannot be reduced to only the integrated functioning of the genome-proteome network, and the cell-stroma interacting system must be taken into consideration in order to give a more reliable picture. As cell form represents the spatial geometric configuration shaped by an integrated set of cellular and environmental cues participating in biological functions control, it is conceivable that fractal-shape parameters could be considered as "omics" descriptors of the cell-stroma system. Within this framework it seems that function follows form, and not the other way around.

Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements

Background

Traditional in vitro cell invasion assays focus on measuring one cell parameter at a time and are often less than ideal in terms of reproducibility and quantification. Further, many techniques are not suitable for quantifying the advancing margin of collectively migrating cells, arguably the most important area of activity during tumor invasion. We have developed and applied a highly quantitative, standardized, reproducible Nest Expansion Assay (NEA) to measure cancer cell invasion in vitro, which builds upon established wound-healing techniques. This assay involves creating uniform circular "nests" of cells within a monolayer of cells using a stabilized, silicone-tipped drill press, and quantifying the margin expansion into an overlaid extracellular matrix (ECM)-like component using computer-assisted applications.

Findings

The NEA was applied to two human-derived breast cell lines, MCF10A and MCF10A-CA1d, which exhibit opposite degrees of tumorigenicity and invasion in vivo. Assays were performed to incorporate various microenvironmental conditions, in order to test their influence on cell behavior and measures. Two types of computer-driven image analysis were performed using Java's freely available ImageJ software and its FracLac plugin to capture nest expansion and fractal dimension, respectively – which are both taken as indicators of invasiveness. Both analyses confirmed that the NEA is highly reproducible, and that the ECM component is key in defining invasive cell behavior. Interestingly, both analyses also detected significant differences between non-invasive and invasive cell lines, across various microenvironments, and over time.

Conclusion

The spatial nature of the NEA makes its outcome susceptible to the global influence of many cellular parameters at once (e.g., motility, protease secretion, cell-cell adhesion). We propose the NEA as a mid-throughput technique for screening and simultaneous examination of factors contributing to cancer cell invasion, particularly suitable for parameterizing and validating Cancer Systems Biology approaches such as mathematical modeling.

Easily adaptable complexity measure for finite time series

We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the widely accepted but conflicting criteria for complexity measurements. Surprisingly, the measure is developed from Kolmogorov complexity, which is traditionally believed to represent only randomness and to satisfy one criterion to the exclusion of the others. For familiar iterative systems, our treatment may imply a heuristic approach to transforming symbolic dynamics into permutation dynamics and vice versa.

Shape factor analysis of progressive rat hepatoma images

We explore the hypothesis that shape factors can be used as tools to probe disease progression in addition to being used for simple classification. We define and apply a new shape factor to digital images of tumor cross sections of progressive rat hepatoma. Using a number of standard pathological measures, each image is also associated with a "disease time," a continuous variable between 0 and 1 with 0 being disease initiation and 1 being a near-fatal condition. The images are converted to data files that represent the 2-D shapes of the tumors. Their shape factors are then determined and plotted versus disease time. The results show that the shape factor can indicate and localize the tumor structural phase transition that occurs between uniform growth and infiltration.

Power Law Analysis Estimates of Analyte Concentration and Particle Size in Highly Scattering Granular Samples from Photon Time-of-Flight Measurements

Optical measurements of particle size and composition in granular samples are difficult to make due to complex light scattering from particles. These multiple scattering events bias absorption estimates and complicate the calculation of scattering and absorption coefficients used to estimate sample properties. Time series data, such as chromatograms and photon time-of-flight (TOF) profiles, contain self-repeating (fractal) characteristics. Power law analysis of photon TOF profiles allows the determination of absorption coefficients and particle sizes in a single experiment. A correlation dimension algorithm was used on photon TOF data from scattering samples. MLR models were then obtained from correlation dimension plots for the estimation of sample properties. Estimates of particle sizes and absorption coefficients were shown to agree well with theoretical values when compared using independent validation sets. Results show close to a 3-fold and up to a 5-fold decrease in the errors of estimation of dye concentration and particle size, respectively, as compared to steady-state measurements. The power law approach provides a useful means of determining sample properties in highly scattering media.