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Computational Models of Brain Energy Metabolism at Different Scales

Cheng, Yougan
http://rave.ohiolink.edu/etdc/view?acc_num=case1396534897

Abstract Details

2014, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
The mathematical modeling of brain energy metabolism in the literature has been approached in a spatially lumped framework, where the region of interest is represented in terms of well mixed compartments representing different cell types, extracellular space and capillary blood. These models shed some light on the brain metabolism, but they cannot account for some potentially important factors including, e.g., the locus of the synaptic activity in reference to capillaries, the effect of diffusion, pre- and postsynaptic neurons, and possible variations in mitochondrial density within the cells. In this thesis, we propose a novel multi-domain formalism to assemble a three dimensional distributed model of brain cellular metabolism, which can take into account some of the aforementioned factors. The model is governed by coupled reaction-diffusion equations in different cells and in the extracellular space, and it allows the inclusion of additional details, for example separate mitochondria for each cell type. This formalism allows to track the changes in metabolites and intermediates in mutually interacting domains without the need for detailed geometric modeling of the microscopic tissue structure. Acknowledging the complexity of the multidimensional model and the difficulty of finding suitable values of many parameters which specify it, we propose a way to reduce the complex model to a lower dimensional one, whose parameter values can be compared with literature values. More specifically, we derive a computational model for a brain sample of the size of a Krogh cylinder, with spatial distribution in tissue along the radial component. For this model, the different availability of oxygen and glucose away from the blood vessel could affect the cells' aerobic or anaerobic metabolism and trigger the uptake of lactate, highlighting the important role of diffusion. This spatially distributed model indicates that drawing conclusions about a complex spatially distributed system from a simplified lumped model may lead to ambiguities. In particular, the results of our simulations suggest that well-mixed models that ignore diffusion may go astray in predictions that involve oxygen. According to our computed examples, the availability of oxygen, more than of glucose, seems to have a stronger role in determining whether the energetic needs will be met with aerobic or anaerobic metabolism. To place complex biological systems in a holistic perspective, it is important to connect parametric models at different scales, understanding how the parameter values and data change with resolution, to avoid erroneous extrapolation. Although the scale change between the lumped model and the distributed model considered in this thesis is relatively small compared to range of spatial scales in biology, going from nanometers to meters, the computed results reveal a significant sensitivity of parameters to scale change. This suggests that simple parameter estimation methods by model fitting may be inadequate, justifying the need for more sophisticated techniques. The results of our simulations offer a possible explanation why experimental data collected under similar conditions may have led to different conclusions when interpreted with models of low resolution, reinforcing the idea that a proper description of biological model parameters is not a single value, but rather a distribution of values.
Daniela Calvetti (Advisor)
Erkki Somersalo (Advisor)
David Gurarie (Committee Member)
Joseph LaManna (Committee Member)
249 p.
Applied Mathematics; Biology; Mathematics
Multi-domain; Reaction-Diffusion Equations; Brain Energy Metabolism; MCMC; Spatially Distributed Models; Optimization

Recommended Citations

Citations

  • Cheng, Y. (2014). Computational Models of Brain Energy Metabolism at Different Scales [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1396534897

    APA Style (7th edition)

  • Cheng, Yougan. Computational Models of Brain Energy Metabolism at Different Scales. 2014. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1396534897.

    MLA Style (8th edition)

  • Cheng, Yougan. "Computational Models of Brain Energy Metabolism at Different Scales." Doctoral dissertation, Case Western Reserve University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396534897

    Chicago Manual of Style (17th edition)

case1396534897
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© 2014, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.