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Objective: An accurate knowledge of energy consumption in burn patients is a prerequisite for rational nutrition therapy. This study sought to create a formula that accounts for the metabolic characteristics of adult burn patients to accurately estimate energy consumption of patients with different areas and extents of burn and at different times after injury., Methods: Resting energy expenditure (REE) data on 66 burn patients, with total body surface area (TBSA) of burns ranging from 4% to 96%, were evaluated at different times after injury. REE values were determined in patients using indirect calorimetry at days 1, 2, 3, 7, 14, 21, and 28 after injury. We then constructed a mathematical model of REE changes post-burn. Next, established two new formulas (one non-linear and the other linear) for energy consumption estimation using model-based analytical solution and regression analysis. The new formulas were compared with measured REE and commonly used formulas including those of Carlson, Xie, Curreri, and Milner to determine accuracy and reliability., Results: Comparative analysis showed that the new formulas offered significantly higher accuracy and reliability than the Milner formula, which is considered the most accurate of commonly used burn energy consumption estimate formulas. The accuracy of the new nonlinear formula (94.29%) and that of the linear formula (91.43%) were significantly higher than that of Milner formula (72.86%) when compared to measured REE (χ2  =  11.706, P  =  0.001; χ2  =  8.230, P  =  0.004, respectively). The reliabilities of the new estimation formulas were both 100% and that of Milner formula was 74.24% (χ2  =  19.513, P  =  0.000)., Conclusion: The new formulas constructed in this study provide reliable simulation of the impact of the degree of burn and post-burn days on energy consumption and offer notably higher accuracy and reliability than other formulas. These formulas will help determine nutritional needs of burn patients., Trial Registration: The study was registered on Chinese Clinical Trial Registry as ChiCTR-TRC-13003806.

Acquiring abundant and high-purity cancer stem cells (CSCs) is an important prerequisite for CSC research. At present, researchers usually gain high-purity CSCs through flow cytometry sorting and expand them by short-term sphere culture. However, it is still uncertain whether we can amplify high-purity CSCs through long-term sphere culture. We have proposed a mathematical model using ordinary differential equations to derive the continuous variation of the CSC ratio in long-term sphere culture and estimated the model parameters based on a long-term sphere culture of MCF-7 stem cells. We found that the CSC ratio in long-term sphere culture presented as gradually decreased drift and might be stable at a lower level. Furthermore, we found that fitted model parameters could explain the main growth pattern of CSCs and differentiated cancer cells in long-term sphere culture.