On the holistic approach in cellular and cancer biology: nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

Diagnostic staging and stratification in psychiatry and oncology: clarifying their conceptual, epistemological and ethical implications

Staging and stratification are two diagnostic approaches that have introduced a more dynamic outlook on the development of diseases, thus participating in blurring the line between the normal and the pathological. First, diagnostic staging, aiming to capture how diseases evolve in time and/or space through identifiable and gradually more severe stages, may be said to lean on an underlying assumption of "temporal determinism". Stratification, on the other hand, allows for the identification of various prognostic or predictive subgroups based on specific markers, relying on a more "mechanistic" or "statistical" form of determinism. There are two medical fields in which these developments have played a significant role and have given rise to sometimes profound nosological transformations: oncology and psychiatry. Drawing on examples from these two fields, this paper aims to provide much needed conceptual clarifications on both staging and stratification in order to outline how several epistemological and ethical issues may, in turn, arise. We argue that diagnostic staging ought to be detached from the assumption of temporal determinism, though it should still play an essential role in adapting interventions to stage. In doing so, it would help counterbalance stratification's own epistemological and ethical shortcomings. In this sense, the reflections and propositions developed in psychiatry can offer invaluable insights regarding how adopting a more transdiagnostic and cross-cutting perspective on temporality and disease dynamics may help combine both staging and stratification in clinical practice.

Future medicine: from molecular pathways to the collective intelligence of the body

The remarkable anatomical homeostasis exhibited by complex living organisms suggests that they are inherently reprogrammable information-processing systems that offer numerous interfaces to their physiological and anatomical problem-solving capacities. We briefly review data suggesting that the multiscale competency of living forms affords a new path for biomedicine that exploits the innate collective intelligence of tissues and organs. The concept of tissue-level allostatic goal-directedness is already bearing fruit in clinical practice. We sketch a roadmap towards 'somatic psychiatry' by using advances in bioelectricity and behavioral neuroscience to design methods that induce self-repair of structure and function. Relaxing the assumption that cellular control mechanisms are static, exploiting powerful concepts from cybernetics, behavioral science, and developmental biology may spark definitive solutions to current biomedical challenges.

Challenges and Limitations of Biological Network Analysis

High-Throughput technologies are producing an increasing volume of data that needs large amounts of data storage, effective data models and efficient, possibly parallel analysis algorithms. Pathway and interactomics data are represented as graphs and add a new dimension of analysis, allowing, among other features, graph-based comparison of organisms’ properties. For instance, in biological pathway representation, the nodes can represent proteins, RNA and fat molecules, while the edges represent the interaction between molecules. Otherwise, biological networks such as Protein–Protein Interaction (PPI) Networks, represent the biochemical interactions among proteins by using nodes that model the proteins from a given organism, and edges that model the protein–protein interactions, whereas pathway networks enable the representation of biochemical-reaction cascades that happen within the cells or tissues. In this paper, we discuss the main models for standard representation of pathways and PPI networks, the data models for the representation and exchange of pathway and protein interaction data, the main databases in which they are stored and the alignment algorithms for the comparison of pathways and PPI networks of different organisms. Finally, we discuss the challenges and the limitations of pathways and PPI network representation and analysis. We have identified that network alignment presents a lot of open problems worthy of further investigation, especially concerning pathway alignment.

Nutrient supply, cell spatial correlation and Gompertzian tumor growth

Gompertzian tumor growth can be reproduced by mitosis, related to nutrient supply, with local spatial cell correlations. The global energy constraint alone does not reproduce in vivo data by the observed values of the nutrient expenditure for the cell activities. The depletion of the exponential growth, described by the Gompertz law, is obtained by mean field spatial correlations or by a small word network among cells. The well-known interdependence between the two parameters of the Gompertz growth naturally emerges and depends on the cell volume and on the tumor density.

Electromagnetic Fields, Genomic Instability and Cancer: A Systems Biological View

This review discusses the use of systems biology in understanding the biological effects of electromagnetic fields, with particular focus on induction of genomic instability and cancer. We introduce basic concepts of the dynamical systems theory such as the state space and attractors and the use of these concepts in understanding the behavior of complex biological systems. We then discuss genomic instability in the framework of the dynamical systems theory, and describe the hypothesis that environmentally induced genomic instability corresponds to abnormal attractor states; large enough environmental perturbations can force the biological system to leave normal evolutionarily optimized attractors (corresponding to normal cell phenotypes) and migrate to less stable variant attractors. We discuss experimental approaches that can be coupled with theoretical systems biology such as testable predictions, derived from the theory and experimental methods, that can be used for measuring the state of the complex biological system. We also review potentially informative studies and make recommendations for further studies.

Advancing Cancer Systems Biology: Introducing the Center for the Development of a Virtual Tumor, CViT

Integrative cancer biology research relies on a variety of data-driven computational modeling and simulation methods and techniques geared towards gaining new insights into the complexity of biological processes that are of critical importance for cancer research. These include the dynamics of gene-protein interaction networks, the percolation of sub-cellular perturbations across scales and the impact they may have on tumorigenesis in both experiments and clinics. Such innovative ‘systems’ research will greatly benefit from enabling Information Technology that is currently under development, including an online collaborative environment, a Semantic Web based computing platform that hosts data and model repositories as well as high-performance computing access. Here, we present one of the National Cancer Institute's recently established Integrative Cancer Biology Programs, i.e. the Center for the Development of a Virtual Tumor, CViT, which is charged with building a cancer modeling community, developing the aforementioned enabling technologies and fostering multi-scale cancer modeling and simulation.

Sensitivity and Specificity of Fractal Analysis to Distinguish Between Healthy and Pathologic Rectal Mucosa Microvasculature Seen During Colonoscopy

PURPOSE

Conventional endoscopy is limited by human capability to recognize and to differentiate pathology. Fractal analysis of blood vessels has been used in other organs, such as the retina, but never before to supplement colonoscopy. The aim of this study was to assess whether it is possible to differentiate between healthy and pathologic rectal mucosa using fractal analysis of the mucosal microvascular architecture seen during colonoscopic examination (Supplemental Digital Content 1, http://links.lww.com/SLE/A145).

METHODS

A total of 300 consecutive patients, 133 females and 167 males with a mean age of 49.1 (±11.3) years, undergoing endoscopy were included in the prospective cohort study. Colonoscopy of the sigmorectal region was performed, and then analyzed with computer-assisted image fractal analysis.

RESULTS

Fractal analysis of mucosal vasculature allowed for differentiation between healthy and pathologic rectal mucosa, as well as different pathologies (P<0.0001). The sensitivity of fractal analysis to diagnose rectal neoplasia was 92.8% to 96.4%, while the specificity was 91.9% to 98.5% depending on the fractal parameter. The sensitivity of fractal analysis to diagnose rectal colitis was 84.2% to 92.1%, while the specificity was 95.0% to 96.0%, depending on the fractal parameter.

CONCLUSIONS

Computer-assisted fractal analysis allows for differentiation between healthy and pathologic rectal mucosa, as well as between different mucosal pathologies, seen during colonoscopy. Fractal analysis improves the sensitivity and specificity of colonoscopy to aid in the diagnosis of neoplasia or colitis, and should be included in the screening and surveillance of these pathologies.

Models for the Study of Whole Systems

This article summarizes a network and complex systems science model for research on whole systems of complementary and alternative medicine (CAM) such as homeopathy and traditional Chinese medicine. The holistic concepts of networks and nonlinear dynamical complex systems are well matched to the global and interactive perspectives of whole systems of CAM, whereas the reductionistic science model is well matched to the isolated local organ, cell, and molecular mechanistic perspectives of pharmaceutically based biomedicine. Whole systems of CAM are not drugs with specific actions. The diagnostic and therapeutic approaches of whole systems of CAM produce effects that involve global and patterned shifts across multiple subsystems of the person as a whole. For homeopathy, several characteristics of complex systems, including the probabilistic nature of attractor patterns, variable sensitivity of complex systems to initial conditions, and emergent behaviors in the evolution of a system in its full environmental context over time, could help account for the mixed basic science and controlled clinical trial research findings, in contrast with the consistently positive outcomes of observational studies in the literature. Application of theories and methods from complex systems and network science can open a new era of advances in understanding factors that lead to good versus poor individual global outcome patterns and to rational triage of patients to one type of care over another. The growing reliance on complex systems thinking and systems biology for cancer research affords a unique opportunity to bridge between the CAM and conventional medical worlds with some common language and conceptual models.

The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas

Background: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas.

Methods: The global fractal capacity D₀, information D₁ and correlation D₂ dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas.

Results: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D₀-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D₁ failed to define the same classes of equivalence. The pairs (D₀, LFD), (D₀, H), (D₀, λ), (D₁, LFD), (D₁, H), (D₁, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D₀ < 1.5820, LFD < 1.3, LCFD > 1.5, H < 0.7, and λ > 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D₀ > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas.

Conclusions: The cut-off D₀-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative criteria based on the complexity and the diversity measures enabled the identification of low or high aggressive prostate carcinomas and should be verified in the future multicenter, randomized studies.

[Fractal geometry in the objective grading of prostate carcinoma]

BACKGROUND

A possible approach to objectively classify complex patterns in tumor tissue is a mathematical and statistical investigation of the distribution of cell nuclei as a geometric representation of cancer cells by fractal dimensions. Both the existence and changes in the fractal structure of tumor tissue have important consequences for the objective system of tumor grading. In addition, the complexity of growth in different carcinomas or their intercellular interactions can be compared to each other.

RESULTS

We present a theoretical introduction into fractal geometry as well as in the computer algorithms based upon the Rényi family of fractal dimensions. Finally, a geometric model of prostate cancer is introduced and the relationship between geometric patterns of prostate tumor and the fractal dimensions of the Rényi family are explained.

Revitalizing personalized medicine: respecting biomolecular complexities beyond gene expression

Despite recent advancements in "omic" technologies, personalized medicine has not realized its fullest potential due to isolated and incomplete application of gene expression tools. In many instances, pharmacogenomics is being interchangeably used for personalized medicine, when actually it is one of the many facets of personalized medicine. Herein, we highlight key issues that are hampering the advancement of personalized medicine and highlight emerging predictive tools that can serve as a decision support mechanism for physicians to personalize treatments.

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.

Self-organization of developing embryo using scale-invariant approach

BACKGROUND

Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.

METHODS

In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.

RESULTS AND CONCLUSION

The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

Some implications of Scale Relativity theory in avascular stages of growth of solid tumors in the presence of an immune system response

We present a traveling-wave analysis of a reduced mathematical model describing the growth of a solid tumor in the presence of an immune system response in the framework of Scale Relativity theory. Attention is focused upon the attack of tumor cells by tumor-infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumor, without necrosis and at some stage prior to (tumor-induced) angiogenesis. For a particular choice of parameters, the underlying system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy and propagation of a perturbation in the tumor cell concentration by cnoidal modes, by depicting spatially heterogeneous tumor cell distributions that are characterized by a relatively small total number of tumor cells. This behavior is consistent with several immunomorphological investigations. Moreover, the alteration of certain parameters of the model is enough to induce soliton like modes and soliton packets into the system, which in turn result in tumor invasion in the form of a standard traveling wave. In the same framework of Scale Relativity theory, a very important feature of malignant tumors also results, that even in avascular stages they might propagate and invade healthy tissues, by means of a diffusion on a Newtonian fluid.

Chinese medicine and biomodulation in cancer patients--Part one

Traditional Chinese Medicine (tcm) may be integrated with conventional Western medicine to enhance the care of patients with cancer. Although tcm is normally implemented as a whole system, recent reductionist research suggests mechanisms for the effects of acupuncture, herbs, and nutrition within the scientific model of biomedicine. The health model of Chinese medicine accommodates physical and pharmacologic interventions within the framework of a body–mind network. A Cartesian split does not occur within this model, but to allow for scientific exploration within the restrictions of positivism, reductionism, and controls for confounding factors, the components must necessarily be separated. Still, whole-systems research is important to evaluate effectiveness when applying the full model in clinical practice. Scientific analysis provides a mechanistic understanding of the processes that will improve the design of clinical studies and enhance safety. Enough preliminary evidence is available to encourage quality clinical trials to evaluate the efficacy of integrating tcm into Western cancer care.

Applications of genome-scale metabolic reconstructions

The availability and utility of genome-scale metabolic reconstructions have exploded since the first genome-scale reconstruction was published a decade ago. Reconstructions have now been built for a wide variety of organisms, and have been used toward five major ends: (1) contextualization of high-throughput data, (2) guidance of metabolic engineering, (3) directing hypothesis-driven discovery, (4) interrogation of multi-species relationships, and (5) network property discovery. In this review, we examine the many uses and future directions of genome-scale metabolic reconstructions, and we highlight trends and opportunities in the field that will make the greatest impact on many fields of biology.

Bacteria as computers making computers

Various efforts to integrate biological knowledge into networks of interactions have produced a lively microbial systems biology. Putting molecular biology and computer sciences in perspective, we review another trend in systems biology, in which recursivity and information replace the usual concepts of differential equations, feedback and feedforward loops and the like. Noting that the processes of gene expression separate the genome from the cell machinery, we analyse the role of the separation between machine and program in computers. However, computers do not make computers. For cells to make cells requires a specific organization of the genetic program, which we investigate using available knowledge. Microbial genomes are organized into a paleome (the name emphasizes the role of the corresponding functions from the time of the origin of life), comprising a constructor and a replicator, and a cenome (emphasizing community-relevant genes), made up of genes that permit life in a particular context. The cell duplication process supposes rejuvenation of the machine and replication of the program. The paleome also possesses genes that enable information to accumulate in a ratchet-like process down the generations. The systems biology must include the dynamics of information creation in its future developments.

Beyond the oncogene paradigm: understanding complexity in cancerogenesis

In the past decades, an enormous amount of precious information has been collected about molecular and genetic characteristics of cancer. This knowledge is mainly based on a reductionistic approach, meanwhile cancer is widely recognized to be a 'system biology disease'. The behavior of complex physiological processes cannot be understood simply by knowing how the parts work in isolation. There is not solely a matter how to integrate all available knowledge in such a way that we can still deal with complexity, but we must be aware that a deeply transformation of the currently accepted oncologic paradigm is urgently needed. We have to think in terms of biological networks: understanding of complex functions may in fact be impossible without taking into consideration influences (rules and constraints) outside of the genome. Systems Biology involves connecting experimental unsupervised multivariate data to mathematical and computational approach than can simulate biologic systems for hypothesis testing or that can account for what it is not known from high-throughput data sets. Metabolomics could establish the requested link between genotype and phenotype, providing informations that ensure an integrated understanding of pathogenic mechanisms and metabolic phenotypes and provide a screening tool for new targeted drug.

Neuronal differentiation and synapse formation in the space-time with temporal fractal dimension

An improvement of the Waliszewski and Konarski approach ([2002] Synapse 43:252-258) to determine the temporal fractal dimension b(t) and scaling factor a(t) for the process of neuronal differentiation and synapse formation in the fractal space-time is presented. In particular the analytical formulae describing the time-dependence of b(t)(t) and a(t)(t), which satisfy the appropriate boundary conditions for t-->0 and t-->infinity, are derived. They have been used to determine the temporal fractal dimension and scaling factor from the two-parametric Gompertz function fitted to experimental data obtained by Jones-Villeneuve et al. ([1982] J Cell Biol 94:253-262) for embryonal carcinoma P19 cells treated by retinoic acid. The results of the calculations differ from those obtained previously by making use of the three- and four-parametric Gompertz function as well as other S-shape functions (Chapman, Hill, Logistic, Sigmoid) evaluated by the fitting of the experimental curve. The temporal fractal dimension can be used as a numerical measure of the neuronal complexity emerging in the process of differentiation, which can be related to the morphofunctional cell organization. A hypothesis is formulated that neuronal differentiation and synapse formation have a lot in common with the process of tumorigenesis. They are qualitatively described by the same Gompertz function of growth and take place in the fractal space-time whose mean temporal fractal dimension is lost during progression.

A stochastic model of cancer initiation including a bystander effect

A stochastic model of cancer initiation is considered. The model is used to evaluate whether a bystander effect may be important in the pre-malignant and malignant stages of carcinogenesis, and furthermore, on the basis of epidemiological data, to estimate the mutation rates of genes involved in the development of oral leukoplakias. The bystander effect is defined here as the capability of oncogenic mutations to increase the mutation probability of neighbouring (bystander) cells, thus leading potentially to a cascade of neighbouring mutated and neoplastic cells as a pre-stage in the development to leukoplakias and cancer. We find that incidence data for oral cancer are indeed in accordance with a significant bystander effect, operating either alone or in combination with genomic instability in the early stages of carcinogenesis, i.e. the development of neoplasia. Simulations performed gave a picture of how mutations and neoplasia may spread in a tissue, to form characteristic leukoplakias with a core of neoplastic cells. The model also showed that the probability of finding at least one neoplastic cell in the tissue after a given number of years is more sensitive to changes in genomic instability within the cell itself than to changes in a bystander effect. Based on epidemiological data we also calculate the maximum number of oncogenic genes that may be involved in the bystander effect and development of genomic instability. Even if capable of explaining the initial development of oncogenic mutations towards neoplastic cells, the bystander model could not reproduce the observed incidence rates of leukoplakia without assuming a carcinogen mutation probability per cell per year of neoplastic cells practically equal to one. This means that the bystander effect, to be of substantial importance in the final development of neoplastic cells towards leukoplakias, requires a very significant increase in mutation probabilities for bystanders to neoplastic cells. Alternatively, additional mechanisms such as abnormal cell differentiation and uncontrolled proliferation and apoptotis in the neoplastic stage may be of major importance during the development to cancerization.

A Global Workspace perspective on mental disorders

Background

Recent developments in Global Workspace theory suggest that human consciousness can suffer interpenetrating dysfunctions of mutual and reciprocal interaction with embedding environments which will have early onset and often insidious staged developmental progression, possibly according to a cancer model, in which a set of long-evolved control strategies progressively fails.

Methods and results

A rate distortion argument implies that, if an external information source carries a damaging 'message', then sufficient exposure to it, particularly during critical developmental periods, is sure to write a sufficiently accurate image of it on mind and body in a punctuated manner so as to initiate or promote similarly progressively punctuated developmental disorder, in essence either a staged failure affecting large-scale brain connectivity, which is the sine qua non of human consciousness, or else damaging the ability of embedding goal contexts to contain conscious dynamics.

Conclusion

The key intervention, at the population level, is clearly to limit exposure to factors triggering developmental disorders, a question of proper environmental sanitation, in a large sense, primarily a matter of social justice which has long been known to be determined almost entirely by the interactions of cultural trajectory, group power relations, and economic structure, with public policy. Intervention at the individual level appears limited to triggering or extending periods of remission, representing reestablishment of an extensive, but largely unexplored, spectrum of evolved control strategies, in contrast with the far better-understood case of cancer.

Spectral markers in preneoplastic intestinal mucosa: an accurate predictor of tumor risk in the MIN mouse

BACKGROUND

We have reported recently that microarchitectural analysis of the histologically normal mucosa using a novel optics technology, four-dimensional elastic light scattering fingerprinting (ELF), provided unprecedented sensitivity for early detection of colon carcinogenesis. In the present study, we explored the ability of four-dimensional ELF to identify an inherited predisposition to colorectal cancer, an issue of considerable importance for optimizing population screening strategies.

METHODS

We used the MIN mouse, a model whose germ line adenomatous polyposis coli truncation leads to spontaneous intestinal tumorigenesis, thus replicating the human syndrome, familial adenomatous polyposis. Spectral markers were assessed by four-dimensional ELF analysis in MIN mice at preneoplastic time points and compared with age-matched controls (C57BL6 mice with wild-type adenomatous polyposis coli). To assess the responsiveness of spectral markers to chemopreventive agents, a subset of MIN mice was supplemented with celecoxib 1,500 ppm.

RESULTS

Spectral slope, fractal dimension, and principal component 3 were dramatically altered in the uninvolved MIN mouse mucosa at the earliest time points. Furthermore, alteration in spectral variables increased over time, consonant with the microarchitectural underpinnings of subsequent tumorigenesis. Additionally, these markers spatially correlated with future adenoma development (small intestine > colon). Short-term treatment with the potent chemopreventive agent, celecoxib, resulted in near normalization of fractal dimension and principal component 3.

CONCLUSIONS

We report, for the first time, that spectral markers, assayed by four-dimensional ELF, were able to sensitively identify a genetic predisposition for intestinal tumorigenesis before the occurrence of phenotypic manifestations. Moreover, the reversal of spectral markers by celecoxib treatment supports the neoplastic relevance.

On time-space of nonlinear phenomena with Gompertzian dynamics

This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: Modulation of apoptosis, proliferation, and fractal dimension

Objectives: Emerging evidence implicates the SNAIL family of transcriptional repressors in cancer development; however, the role of SNAIL in colorectal cancer has not been established. To investigate the importance of SNAIL in colorectal carcinogenesis, we examined the phenotypic and cellular consequences of SNAIL down-regulation in the MIN mouse. Methods: Twenty-eight male MIN mice were randomized to treatment with an antisense phosphorodiamidate morpholino oligomer (AS-PMO) to SNAIL, saline, or a scrambled sequence control for 6 weeks. Tumors were scored and the molecular/cellular effects of anti-SNAIL treatment were evaluated through immunohistochemical analysis of the uninvolved intestinal mucosa for SNAIL and E-cadherin levels along with rates of apoptosis and proliferation. Furthermore, microarchitectural alterations were determined through measurement of fractal dimension. Results: In the uninvolved mucosa, SNAIL AS-PMO treatment moderately decreased SNAIL protein when compared with saline-treated animals (immunohistochemistry scores 3.0 ± 0.8 versus 2.1 ± 0.6, respectively; P = 0.01) with a concomitant increase in E-cadherin expression (1.8 ± 0.6 versus 2.4 ± 0.5; P &lt; 0.05). Anti-SNAIL PMO, but not scramble control, resulted in a significant decrease in both total tumor number and incidence of tumors &gt;2 mm (22% and 54%, respectively; P &lt; 0.05). Furthermore, this was accompanied by an increased apoptosis rate (2-fold), decreased proliferation (3-fold), and normalization of the fractal dimension in the uninvolved intestinal mucosa. Conclusions: We show, for the first time, that SNAIL overexpression is important in intestinal tumorigenesis. While this PMO regimen afforded modest SNAIL suppression and hence tumor reduction, this provides compelling evidence for the role of SNAIL overexpression in colonic neoplasia.

Coherent states of Gompertzian growth

The origin of the Gompertz function G(t)=G(0)e(b/a(1-e(-at))) widely applied to fit the biological and medical data, particularly growth of organisms, organs, and tumors is analyzed. It is shown that this function is a solution of a time-dependent counterpart of the Schrödinger equation for the Morse oscillator with anharmonicity constant equal to 1. The coherent states of the Gompertzian systems, which minimize the time-energy uncertainty relation, have been found. These are eigenstates of the annihilation operator identified with the operator of growth, whereas eigenstates of the creation operator represent the Gompertzian states of regression. The coherent formation of the specific growth patterns in the Gompertzian systems appears as a result of the nonlocal long-range cooperation between the microlevel (the individual cell) and the macrolevel (the system as a whole).

Emerging patterns in tumor systems: simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model

Brain cancer cells invade early on surrounding parenchyma, which makes it impossible to surgically remove all tumor cells and thus significantly worsens the prognosis of the patient. Specific structural elements such as multicellular clusters have been seen in experimental settings to emerge within the invasive cell system and are believed to express the systems' guidance toward nutritive sites in a heterogeneous environment. Based on these observations, we developed a novel agent-based model of spatio-temporal search and agglomeration to investigate the dynamics of cell motility and aggregation with the assumption that tumors behave as complex dynamic self-organizing biosystems. In this model, virtual cells migrate because they are attracted by higher nutrient concentrations and to avoid overpopulated areas with high levels of toxic metabolites. A specific feature of our model is the capability of cells to search both globally and locally. This concept is applied to simulate cell-surface receptor-mediated information processing of tumor cells such that a cell searching for a more growth-permissive place "learns" the information content of a brain tissue region within a two-dimensional lattice in two stages, processing first the global and then the local input. In both stages, differences in microenvironment characteristics define distinctions in energy expenditure for a moving cell and thus influence cell migration, proliferation, agglomeration, and cell death. Numerical results of our model show a phase transition leading to the emergence of two distinct spatio-temporal patterns depending on the dominant search mechanism. If global search is dominant, the result is a small number of large clusters exhibiting rapid spatial expansion but shorter lifetime of the tumor system. By contrast, if local search is dominant, the trade-off is many small clusters with longer lifetime but much slower velocity of expansion. Furthermore, in the case of such dominant local search, the model reveals an expansive advantage for tumor cell populations with a lower nutrient-depletion rate. Important implications of these results for cancer research are discussed.

The device and algorithm for estimation of the mechanoemisson chaos in blood of patients with gastric cancer

The mechanoemission (ME) of blood is developed as a result of mechanochemical activation of a sample which is layered onto chromatographic paper. This paper describes computer-controlled device, aimed for generation, detection and analysis of ME data in the blood of the persons investigated. The original algorithm for estimation of ME chaos in blood is developed. For gastric cancer patients an increase of ME chaos is observed in comparison with healthy individuals and patients with inflammation of gastric mucosa. The concept of deterministic chaos is biohierarchical for the host of a cancer patient. In the light of this we have calculated that spatial chaos for gastric cancer patients is also increased in the geometrical structure of tumor cells and magnetic resonance imaging of the stomach. The concept of deterministic chaos may find an application in the development of new multi-computer organizations for medical diagnostic equipment.

Neuronal differentiation and synapse formation occur in space and time with fractal dimension

The analysis of a set of experimental data obtained by an independent team of researchers confirms that neuronal differentiation or synapse formation do occur in time and space with fractal dimension. The interacting cells create first a dynamic system with its own attractor, (i.e., a fragment of time and space where the dynamic processes occur and where no further evolution of the system is possible at all owing to the action of the intrasystemic forces unless some extrasystemic forces act upon it). This attractor is then modified in the active manner by the differentiating cells until the system attains a degenerated stationary state and differentiation ends. The fractal structure of the system is also lost in the course of tumor progression. Our data indicate that the cellular system can attain the degenerated stationary state, leaving the attractor with a fractal dimension directly or undergoing diversification into many attractors and going through the areas of deterministic chaos. Since evolution of the cellular system is driven by the cooperative dynamic processes, as reflected by the changes of the mean fractal dimension between the intervals of the Gompertzian curve, it is likely that cells differentiate into neurons and create synapses with a conjugated probability and non-Gaussian distribution rather than with the classical probability and the Gaussian distribution. These findings can help to optimize features of artificial neural networks. They also define a simple in vitro biological model for biophysical and biochemical studies on natural neural networks.

Annotated bibliography of chaos for occupational therapy

Given the level of complexity at which the practice of occupational therapy operates, chaos may be the key to fresh insight into the nature of occupation. This article, through an innovative scholarly format-the annotation-presents essential concepts of chaos theory which are relevant for occupational therapy. A rationale for the importance of chaos theory and complexity science is presented and the limited extent to which chaos theory has been addressed in the occupational therapy literature is identified. Occupational therapy links to chaos and complexity are delineated and explained based upon a review of fourteen articles appearing in peer reviewed journals over a five year period (1993-1998), which are presented in three categories: (a) interdisciplinary applications, (b) mental health and creativity applications, and (c) educational and research applications. Conclusions about the relevance of chaos theory to occupational therapy are presented in the last section of the paper.

A review of analytical techniques for gait data. Part 1: Fuzzy, statistical and fractal methods

In recent years, several new approaches to gait data analysis have been explored, including fuzzy systems, multivariate statistical techniques and fractal dynamics. Through a critical survey of recent gait studies, this paper reviews the potential of these methods to strengthen the gait laboratory's analytical arsenal. It is found that time-honoured multivariate statistical methods are the most widely applied and understood. Although initially promising, fuzzy and fractal analyses of gait data remain largely unknown and their full potential is yet to be realized. The trend towards fusing multiple techniques in a given analysis means that additional research into the application of these two methods will benefit gait data analysis.

Tissue as a self-organizing system with fractal dynamics

Cell is a supramolecular dynamic network. Screening of tissue-specific cDNA library and results of Relative RT-PCR indicate that the relationship between genotype, (i.e., dynamic network of genes and their protein regulatory elements) and phenotype is non-bijective, and mendelian inheritance is a special case only. This implies non-linearity, complexity, and quasi-determinism, (i.e., co-existence of deterministic and non-deterministic events) of dynamic cellular network; prerequisite conditions for the existence of fractal structure. Indeed, the box counting method reveals that morphological patterns of the higher order, such as gland-like structures or populations of differentiating cancer cells possess fractal dimension and self-similarity. Since fractal space is not filled out randomly, a variety of morphological patterns of functional states arises. The expansion coefficient characterizes evolution of fractal dynamics. The coefficient indicates what kind of interactions occurs between cells, and how far from the limiting integer dimension of the Euclidean space the expanding population of cells is. We conclude that cellular phenomena occur in the fractal space; aggregation of cells is a supracollective phenomenon (expansion coefficient > 0), and differentiation is a collective one (expansion coefficient < 0). Fractal dimension or self-similarity are lost during tumor progression. The existence of fractal structure in a complex tissue system denotes that dynamic cellular phenomena generate an attractor with the appropriate organization of space-time. And vice versa, this attractor sets up physical limits for cellular phenomena during their interactions with various fields. This relationship can help to understand the emergence of extraterrestial forms of life. Although those forms can be composed of non-carbon molecules, fractal structure appears to be the common feature of all interactive biosystems.

Simulated brain tumor growth dynamics using a three-dimensional cellular automaton

We have developed a novel and versatile three-dimensional cellular automaton model of brain tumor growth. We show that macroscopic tumor behavior can be realistically modeled using microscopic parameters. Using only four parameters, this model simulates Gompertzian growth for a tumor growing over nearly three orders of magnitude in radius. It also predicts the composition and dynamics of the tumor at selected time points in agreement with medical literature. We also demonstrate the flexibility of the model by showing the emergence, and eventual dominance, of a second tumor clone with a different genotype. The model incorporates several important and novel features, both in the rules governing the model and in the underlying structure of the model. Among these are a new definition of how to model proliferative and non-proliferative cells, an isotropic lattice, and an adaptive grid lattice.

Genetic analysis of multiple synchronous lesions of the colon adenoma-carcinoma sequence

The colorectal adenoma-carcinoma sequence represents a well-known paradigm for the sequential development of cancer driven by the accumulation of genomic defects. Although the colorectal adenoma-carcinoma sequence is well investigated, studies about tumours of different dignity co-existent in the same patient are seldom. In order to address the distribution of genetic alterations in different lesions of the same patient, we coincidently investigated carcinomas, adenomas and aberrant crypt foci in patients with sporadic colon cancer. By utilizing polymerase chain reaction, single-strand conformation polymorphism, heteroduplex-analysis, restriction fragment length polymorphism, protein truncation test and sequencing techniques we looked for mutations and microsatellite instability of APC, H-ras, K-ras, p53, DCC and the DNA repair genes hMLH1/hMSH2. In accordance with the suggested adenoma-carcinoma sequence of the colon, four patients reflected the progressive accumulation of genetic defects in synchronously appearing tumours during carcinogenesis. However, two patients with non-hereditary malignomas presented different genetic instabilities in different but synchronously appearing tumours suggesting non-clonal growth under almost identical conditions of the environment. Thus, sporadically manifesting multiple lesions of the colon were not necessarily driven by similar genetic mechanisms. Premalignant lesions may transform into malignant tumours starting from different types of genetic instability, which indicates independent and simultaneous tumorigenesis within the same organ.

Cellular automaton of idealized brain tumor growth dynamics

A novel cellular automaton model of proliferative brain tumor growth has been developed. This model is able to simulate Gompertzian tumor growth over nearly three orders of magnitude in radius using only four microscopic parameters. The predicted composition and growth rates are in agreement with a test case pooled from the available medical literature. The model incorporates several new features, improving previous models, and also allows ready extension to study other important properties of tumor growth, such as clonal competition.

Distribution of gland-like structures in human gallbladder adenocarcinomas possesses fractal dimension

BACKGROUND AND OBJECTIVES

Epithelial cells form tissue patterns of higher order such as gland-like structures. A question arises whether distribution of those patterns in adenocarcinomas is subject to certain regularity.

METHODS

Due to the pilot nature of this study, gallbladder adenocarcinomas were preselected by histopathological, immunohistochemical, and morphometric analysis to ensure relative homogeneity of the patterns analyzed. A box-counting method was applied to investigate a relationship between a number of gland-like structures and a radius of the expanding family of the concentric circles.

RESULTS

The coefficient of linear regression characterizing that relationship possesses noninteger value. It is 1. 585 (well-differentiated adenocarcinomas, standard deviation (SD) = 0.038, n = 100 sections), and 1.340 (moderately differentiated adenocarcinomas, SD = 0.044, n = 100 sections). While both nuclear area and nucleo-cytoplasmic ratio in those tissues remain within a similar range (Analysis of Variance (ANOVA), F(0) = 0.791 < F(alpha) = 3.84, P = 3 x 10(-3) and F(0) = 0.077 < F(alpha) = 3.84, P = 10(-6), respectively, for k = 20,000 cells, in which F(0) is a value of the test function, F(alpha) is a critical, limit value of the F-test at the constant confidence value alpha = 0.05), a difference of fractal dimension is significant (F(0) = 3.94 > F(alpha) = 0.693, n = 100 sections, P = 2 x 10(-3)). Also, variablity of fractal dimension between tumor sections is significant (moderately differentiated adenocarcinomas, F(0) = 1.9856 > F(alpha) = 1.4262, n = 100 sections, P = 0.189).

CONCLUSIONS

There is fractal regularity in distribution of gland-like structures in human gallbladder adenocarcinomas. Fractal dimension is a holistic parameter which can be applied to evaluate tumor grading in a quantitative manner.