Browsing by Subject "Scale Invariance"

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    Metabolic alterations associated with hemorrhagic shock and traumatic injury as measured in the urine.
    (2011-12) Lusczek, Elizabeth Rose
    Introduction: This dissertation focuses on profiling the changes in metabolism that occur as a result of hemorrhagic shock and traumatic injury as observed in urine obtained from a porcine model. Hemorrhagic shock and traumatic injury are responsible for the majority of deaths under the age of 44. A porcine model of hemorrhagic shock and traumatic injury was used to examine changes in metabolism due to hemorrhagic shock and traumatic injury. Changes in metabolism were hypothesized to be dependent upon the metabolic state the animal occupies upon injury (fed or fasted). It was also hypothesized that a metabolite or metabolites could serve as a marker of mortality. Materials and Methods: Nuclear magnetic resonance (NMR) spectroscopy and Chenomx software were used to generate individual profiles of metabolite concentrations (the metabolome) for each urine sample obtained. Because hemorrhagic shock produces drastic changes in urine concentration and large fluctuations in the concentrations of endogenous metabolites in the urine, urine must be normalized to urine output to allow for accurate comparisons between urine samples. The urinary metabolome was analyzed with partial least squares discriminant analysis (PLS-DA) and with a scale-free network. Results: PLS-DA models showed that metabolites associated with respiration, ischemia/reperfusion injury, and cell membrane damage were observed in the urine two hours after the initiation of resuscitation. Other metabolites which may be associated with injury sustained from surgical preparation were observed at 20 hours after the initiation of resuscitation. The metabolites 1,6-Anhydro β-D-glucose and mannose were associated with the metabolome of fed animals. The network analysis of the metabolome is reflective of the scale-invariant nature of metabolism. Respiratory metabolites were separated by whether they are involved in aerobic or anaerobic respiration. Anaerobic metabolites were also associated with markers of cell membrane rupture. Lactate, pyruvate, 2-oxoglutarate, succinate, taurine, glycine, dimethylamine, and creatinine were identified as well-connected hub metabolites in the network. No metabolites were associated with survival alone. Conclusions: The pathophysiology associated with hemorrhagic shock can be treated as a scale invariant process particularly with respect to metabolism. Results from a traditional metabolomics treatment of the data with PLS-DA models were congruent with results from a scale-invariant, weakly modular network of the urinary metabolome. Other samples obtained from these experiments (muscle, liver, and serum) could benefit from a similar treatment. Additional work in (a) integrating the metabolomes of all four biological samples and (b) creating a physics-based theory of hemorrhagic shock may provide important information about mortality and the propagation of injury.
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    Scale invariance and scaling breaks - new metrics for inferring process signature from high resolution LiDAR topography.
    (2009-10) Gangodagamage, Chandana
    Landscapes posses many scales of variability, from hillslopes to the river network structure, and have been the subject of intense research over the past three decades. Despite this tremendous variability, it has been well documented by now that scale-invariances do exist in several landscape attributes reflecting the natural organization of processes responsible for the formation of those landscapes. The availability of very high resolution (sub-meter scale) digital topography data from laser altimetry (LiDAR) offers an unprecedented opportunity to probe into the structure of landscapes at scales never imagined before and extract properties useful for modeling water, sediment, and nutrient fluxes in a watershed. In this work, we take advantage of these high resolution topography data to introduce new metrics for quantifying landscape organization and explore scaling laws across the continuum of hillslope-fluvial regimes. The innovations we introduce rely on: (1) adapting a new scale parameter which we call ``directed distance from the divide'' which allows examining divergent and convergent parts of the landscape under a single framework; (2) using this new scale parameter to identify the signature of landslides on a landscape allowing thus an objective mapping of those landslides; (3) introduction of the ``incremental drainage area'' function along the mainstream to quantify the hierarchy and clustering of tributaries; and (4) introduction of an non-traditional horizontal function that measures ``valley width''as one fills up the channels beyond their banks and maps the left and right extend of the landscape. A common theme in all of the above developments is the quest for mapping the complex three dimensional structure of landscapes onto simpler, preferably one dimensional, functions that reflect different aspects of the landscape organization. Once this is accomplished, our common method of analysis relies on the theory of multi-scaling using wavelets, i.e., in quantifying how the statistical structure of the extracted attributes changes when one sees them at different scales.