Brain Model Based on the Canonical Ensemble with Functional MRI: A Thermodynamic Exploration of the Neural System

Objective. System modeling is an important method to study the working mechanisms of the brain. This study attempted to build a model of the brain from the perspective of thermodynamics at the system level, which brought a new perspective to brain modeling. Approach. Regarding brain regions as systems, voxels as particles, and intensity of signals as energy of particles, the thermodynamic model of the brain was built based on the canonical ensemble theory. Two pairs of activated regions and two pairs of inactivated brain regions were selected for comparison in this study, and the thermodynamic properties based on the proposed model were analyzed. In addition, the thermodynamic properties were extracted as input features for the detection of Alzheimer’s disease. Main Results. The experimental results verified the assumption that the brain follows thermodynamic laws. This demonstrated the feasibility and rationality of the proposed brain thermodynamic modeling method, indicating that thermodynamic parameters drawn from our model can be applied to describe the state of the neural system. Meanwhile, the brain thermodynamic model achieved good accuracy in the detection of Alzheimer’s disease, suggesting the potential application of thermodynamic models in auxiliary diagnosis. Significance. (1) In the previous studies, only some thermodynamic parameters in physics were analogized and applied to brain image analysis, while, in this study, a complete system model of the brain was proposed through the principles of thermodynamics. And, based on the neural system models proposed, thermodynamic parameters were obtained to describe the observation and evolution of the neural system. (2) Based on the proposed thermodynamic models, we found and confirmed that the neural system also follows the laws of thermodynamics: the activation of system always leads to increased internal energy, increased free energy, and decreased entropy as what is discovered in many other systems besides classic thermodynamic system. (3) The detection of neural disease was demonstrated to benefit from the thermodynamic model, which confirmed that the thermodynamic model proposed can indeed describe the evolution of the neural system diseases. And it further implied the immense potential of thermodynamics in auxiliary diagnosis.

A Comparative Evaluation of Thermodynamic Models for Prediction of Wax Deposition

Wax deposition on inner surfaces of pipelines is a costly problem for the petroleum industry. This flow assurance problem is of particular interest during the production and transportation of waxy oils in cold environments. An understanding of known mechanisms and available thermodynamic models will be useful for the management and planning of mitigation strategies for wax deposition. This paper presents a critical review of wax prediction models used for estimation of wax deposition based on chemical hydrocarbon compositions and thermobaric condition. The comparative analysis is applied to highlight the effective mechanisms guiding the wax deposition, and how this knowledge can be used to model and provide solutions to reducing wax deposition issues. One group of thermodynamic models assume that the precipitated wax is a solid solution. These models are divided into two categories: ideal (Erickson and Pedersen models) and non-ideal solutions (Won and Coutinho models). In the other group of models, the wax phase consists of many solid phases (Lira-Galeana model). The authors summarized the limitations of the models, evaluated, and identified ways to represent the overview of existing thermodynamical models for predicting wax precipitation. Within the strong demand from industry, the results of this manuscript can aid to aspire engineers and researcher.