The Fractal Tapestry of Life: II Entailment of Fractional Oncology by Physiology Networks

Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra

Biological and psychological processes have been conceptualized as emerging from intricate multiplicative interactions among component processes across various spatial and temporal scales. Among the statistical models employed to approximate these intricate nonlinear interactions across scales, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, several fundamental questions persist concerning the proper interpretations of multifractal evidence of nonlinear cross-scale interactivity. Does multifractal spectrum width depend on multiplicative interactions, constituent noise processes participating in those interactions, or both? We conducted numerical simulations of cascade time series featuring component noise processes characterizing a range of nonlinear temporal correlations: nonlinearly multifractal, linearly multifractal (obtained via the iterative amplitude adjusted wavelet transform of nonlinearly multifractal), phase-randomized linearity (obtained via the iterative amplitude adjustment Fourier transform of nonlinearly multifractal), and phase and amplitude randomized (obtained via shuffling of nonlinearly multifractal). Our findings show that the multiplicative interactions coordinate with the nonlinear temporal correlations of noise components to dictate emergent multifractal properties. Multiplicative cascades with stronger nonlinear temporal correlations make multifractal spectra more asymmetric with wider left sides. However, when considering multifractal spectral differences between the original and surrogate time series, even multiplicative cascades produce multifractality greater than in surrogate time series, even with linearized multifractal noise components. In contrast, additivity among component processes leads to a linear outcome. These findings provide a robust framework for generating multifractal expectations for biological and psychological models in which cascade dynamics flow from one part of an organism to another.

A scale-free model of acute and ventilator-induced lung injury: a network theory approach inspired by seismology

Introduction

Acute respiratory distress syndrome (ARDS) presents a significant clinical challenge, with ventilator-induced lung injury (VILI) being a critical complication arising from life-saving mechanical ventilation. Understanding the spatial and temporal dynamics of VILI can inform therapeutic strategies to mitigate lung damage and improve outcomes.

Methods

Histological sections from initially healthy mice and pulmonary lavage-injured mice subjected to a second hit of VILI were segmented with Ilastik to define regions of lung injury. A scale-free network approach was applied to assess the correlation between injury regions, with regions of injury represented as 'nodes' in the network and 'edges' quantifying the degree of correlation between nodes. A simulated time series analysis was conducted to emulate the temporal sequence of injury events.

Results

Automated segmentation identified different lung regions in good agreement with manual scoring, achieving a sensitivity of 78% and a specificity of 85% across 'injury' pixels. Overall accuracy across 'injury', 'air', and 'other' pixels was 81%. The size of injured regions followed a power-law distribution, suggesting a 'rich-get-richer' phenomenon in the distribution of lung injury. Network analysis revealed a scale-free distribution of injury correlations, highlighting hubs of injury that could serve as focal points for therapeutic intervention. Simulated time series analysis further supported the concept of secondary injury events following an initial insult, with patterns resembling those observed in seismological studies of aftershocks.

Conclusion

The size distribution of injured regions underscores the spatially heterogeneous nature of acute and ventilator-induced lung injury. The application of network theory demonstrates the emergence of injury 'hubs' that are consistent with a 'rich-get-richer' dynamic. Simulated time series analysis demonstrates that the progression of injury events in the lung could follow spatiotemporal patterns similar to the progression of aftershocks in seismology, providing new insights into the mechanisms of injury distribution and propagation. Both phenomena suggest a potential for interventions targeting these injury 'hubs' to reduce the impact of VILI in ARDS management.

Complexity Synchronization of Organ Networks

The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the 'complexity matching effect', and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks' multifractal dimensions.

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.