Self-organizing cultured neural networks: Image analysis techniques for longitudinal tracking and modeling of the underlying network structure

Esta tesis estudia la evolución estructural de conjuntos de neuronas como la capacidad de auto-organización desde conjuntos de neuronas separadas hasta que forman una red (clusterizada) compleja. Esta tesis contribuye con el diseño e implementación de un algoritmo no supervisado de segmentación basado en grafos con un coste computacional muy bajo. Este algoritmo proporciona de forma automática la estructura completa de la red a partir de imágenes de cultivos neuronales tomadas con microscopios de fase con una resolución muy alta. La estructura de la red es representada mediante un objeto matemático (matriz) cuyos nodos representan a las neuronas o grupos de neuronas y los enlaces son las conexiones reconstruidas entre ellos. Este algoritmo extrae también otras medidas morfológicas importantes que caracterizan a las neuronas y a las neuritas. A diferencia de otros algoritmos hasta el momento, que necesitan de fluorescencia y técnicas inmunocitoquímicas, el algoritmo propuesto permite el estudio longitudinal de forma no invasiva posibilitando el estudio durante la formación de un cultivo. Además, esta tesis, estudia de forma sistemática un grupo de variables topológicas que garantizan la posibilidad de cuantificar e investigar la progresión de las características principales durante el proceso de auto-organización del cultivo. Nuestros resultados muestran la existencia de un estado concreto correspondiente a redes con configuracin small-world y la emergencia de propiedades a micro- y meso-escala de la estructura de la red. Finalmente, identificamos los procesos físicos principales que guían las transformaciones morfológicas de los cultivos y proponemos un modelo de crecimiento de red que reproduce el comportamiento cuantitativamente de las observaciones experimentales. ABSTRACT The thesis analyzes the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. In particular, it contributes with the design and implementation of a graph-based unsupervised segmentation algorithm, having an associated very low computational cost. The processing automatically retrieves the whole network structure from large scale phase-contrast images taken at high resolution throughout the entire life of a cultured neuronal network. The network structure is represented by a mathematical object (a matrix) in which nodes are identified neurons or neurons clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocyto- chemistry techniques, our measures are non invasive and entitle us to carry out a fully longitudinal analysis during the maturation of a single culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main networks characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graphs micro- and meso-scale properties emerge. Finally, we identify the main physical processes taking place during the cultures morphological transformations, and embed them into a simplified growth model that quantitatively reproduces the overall set of experimental observations.

Self-organizing cultured neural networks: Image analysis techniques for longitudinal tracking and modeling of the underlying network structure (versión actualizada)

Esta tesis estudia la evolución estructural de conjuntos de neuronas como la capacidad de auto-organización desde conjuntos de neuronas separadas hasta que forman una red (clusterizada) compleja. Esta tesis contribuye con el diseño e implementación de un algoritmo no supervisado de segmentación basado en grafos con un coste computacional muy bajo. Este algoritmo proporciona de forma automática la estructura completa de la red a partir de imágenes de cultivos neuronales tomadas con microscopios de fase con una resolución muy alta. La estructura de la red es representada mediante un objeto matemático (matriz) cuyos nodos representan a las neuronas o grupos de neuronas y los enlaces son las conexiones reconstruidas entre ellos. Este algoritmo extrae también otras medidas morfológicas importantes que caracterizan a las neuronas y a las neuritas. A diferencia de otros algoritmos hasta el momento, que necesitan de fluorescencia y técnicas inmunocitoquímicas, el algoritmo propuesto permite el estudio longitudinal de forma no invasiva posibilitando el estudio durante la formación de un cultivo. Además, esta tesis, estudia de forma sistemática un grupo de variables topológicas que garantizan la posibilidad de cuantificar e investigar la progresión de las características principales durante el proceso de auto-organización del cultivo. Nuestros resultados muestran la existencia de un estado concreto correspondiente a redes con configuracin small-world y la emergencia de propiedades a micro- y meso-escala de la estructura de la red. Finalmente, identificamos los procesos físicos principales que guían las transformaciones morfológicas de los cultivos y proponemos un modelo de crecimiento de red que reproduce el comportamiento cuantitativamente de las observaciones experimentales. ABSTRACT The thesis analyzes the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. In particular, it contributes with the design and implementation of a graph-based unsupervised segmentation algorithm, having an associated very low computational cost. The processing automatically retrieves the whole network structure from large scale phase-contrast images taken at high resolution throughout the entire life of a cultured neuronal network. The network structure is represented by a mathematical object (a matrix) in which nodes are identified neurons or neurons clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocyto- chemistry techniques, our measures are non invasive and entitle us to carry out a fully longitudinal analysis during the maturation of a single culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main networks characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graphs micro- and meso-scale properties emerge. Finally, we identify the main physical processes taking place during the cultures morphological transformations, and embed them into a simplified growth model that quantitatively reproduces the overall set of experimental observations.

Modeling GHG emissions, N and C dynamics in Spanish agricultural soils.

To date, only few initiatives have been carried out in Spain in order to use mathematical models (e.g. DNDC, DayCent, FASSET y SIMSNIC) to estimate nitrogen (N) and carbon (C) dynamics as well as greenhouse gases (GHG) in Spanish agrosystems. Modeling at this level may allow to gain insight on both the complex relationships between biological and physicochemical processes, controlling the processes leading to GHG production and consumption in soils (e.g. nitrification, denitrification, decomposing, etc.), and the interactions between C and N cycles within the different components of the continuum plant-soil-environment. Additionally, these models can simulate the processes behind production, consumition and transport of GHG (e.g. nitrous oxide, N2O, and carbon dioxide, CO2) in the short and medium term and at different scales. Other sources of potential pollution from soils can be identified and quantified using these process-based models (e.g. NO3 y NH3).

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Blood flow and oxygen delivery to human brain during functional activity: Theoretical modeling and experimental data

Coupling of cerebral blood flow (CBF) and cerebral metabolic rate for oxygen (CMRO2) in physiologically activated brain states remains the subject of debates. Recently it was suggested that CBF is tightly coupled to oxidative metabolism in a nonlinear fashion. As part of this hypothesis, mathematical models of oxygen delivery to the brain have been described in which disproportionately large increases in CBF are necessary to sustain even small increases in CMRO2 during activation. We have explored the coupling of CBF and oxygen delivery by using two complementary methods. First, a more complex mathematical model was tested that differs from those recently described in that no assumptions were made regarding tissue oxygen level. Second, [15O] water CBF positron emission tomography (PET) studies in nine healthy subjects were conducted during states of visual activation and hypoxia to examine the relationship of CBF and oxygen delivery. In contrast to previous reports, our model showed adequate tissue levels of oxygen could be maintained without the need for increased CBF or oxygen delivery. Similarly, the PET studies demonstrated that the regional increase in CBF during visual activation was not affected by hypoxia. These findings strongly indicate that the increase in CBF associated with physiological activation is regulated by factors other than local requirements in oxygen.

Self-heating and deicing conductive cement. Experimental study and modeling

This research studies the self-heating produced by the application of an electric current to conductive cement pastes with carbonaceous materials. The main parameters studied were: type and percentage of carbonaceous materials, effect of moisture, electrical resistance, power consumption, maximum temperature reached and its evolution and ice melting kinetics are the main parameters studied. A mathematical model is also proposed, which predicts that the degree of heating is adjustable with the applied voltage. Finally, the results have been applied to ensure that cementitious materials studied are feasible to control ice layers in transportation infrastructures.

Empirical crash injury modeling and vehicle-size mix. Technical report.

Mode of access: Internet.

Problem definition and modeling techniques for the study of Kaneohe Bay, Oahu, Hawaii : final report /

Cover title.

Improvement of mathematical models for simulation of vehicle handling. Volume 6: programmers' guide for the driver module. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 7: technical manual for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 8: summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Preliminary development - head-neck simulator. Volume II: mathematical simulations. Final report.

National Highway Traffic Safety Administration, Vehicle Research and Test center, East Liberty, Ohio