Background: Cancer, a complex and deadly health concern today, is characterized by forming potentially malignant tumors or cancer cells. The dynamic interaction between these cells and their environment is crucial to the disease. Mathematical models can enhance our understanding of these interactions, helping us predict disease progression and treatment strategies. Methods: In this study, we develop a fractional tumor-immune interaction model specifically for lung cancer (FTIIM-LC). We present some definitions and significant results related to the Caputo operator. We employ the generalized Laguerre polynomials (GLPs) method to find the optimal solution for the FTIIM-LC model. We then conduct a numerical simulation and compare the results of our method with other techniques and real-world data. Results: We propose a FTIIM-LC model in this paper. The approximate solution for the proposed model is derived using a series of expansions in a new set of polynomials, the GLPs. To streamline the process, we integrate Lagrange multipliers, GLPs, and operational matrices of fractional and ordinary derivatives. We conduct a numerical simulation to study the effects of varying fractional orders and achieve the expected theoretical results. Conclusion: The findings of this study demonstrate that the optimization methods used can effectively predict and analyze complex phenomena. This innovative approach can also be applied to other nonlinear differential equations, such as the fractional Klein–Gordon equation, fractional diffusion-wave equation, breast cancer model, and fractional optimal control problems.

The primary function of the human respiratory system is gas and moisture exchange, and conditioning inhaled air to prevent damage to the lungs and alveoli. In a fire incident, exposed soft tissues contract and the respiratory system may be severely damaged, possibly leading to respiratory failure and even respiratory arrest. The purpose of this study is to numerically simulate hot airflow in the human upper airway and trachea to investigate heat and moisture transfer and induced thermal injuries. For analysis, the airflow is assumed to be laminar and steady, and simulations have been carried out at volume flow rates of 5 and 10 L/min, inlet temperatures of 70-240 °C, and relative humidity up to 40%. The mucous layer and surrounding tissues are incorporated into the conducting zone of the model. The blood perfusion is considered at different rates up to 5(Kg/m³.s) to regulate the temperature, and the vapor concentration is coupled with the energy equation. The temperature and humidity distribution on the airway wall were calculated for all the studied conditions in order to find the mild and severe burn for different inhaled air temperatures. At the inlet temperatures of 70 and 100 °C, there are mild burns in several nasal cavity regions. At the higher temperatures of 160 and 200 °C, these areas suffer from severe burns and mild burns occur at the superior parts and nasopharynx. Rapid evaporation and tissue destruction will be observed if anyone breathes the 240 °C air. The results show that the hot inlet temperatures drop below 44 °C when passing through the upper airway, and the lower airway was not affected. Increasing the inlet temperature from 70 to 240 °C extends the burns from mild to severe and the affected areas from the beginning of the nasal cavity to the pharynx.

Background: Sleep disturbances are common among uremic patients. However, limited data are available on predictors of the quality of sleep in this population. Objectives: This study aimed to assess the quality of sleep in patients undergoing hemodialysis and investigate its predictors. Methods: In this cross-sectional study, 197 patients on maintenance hemodialysis were consecutively included from three medical centers in Shiraz, southern Iran. They completed the Pittsburgh sleep quality index. Serum calcium, phosphorus, and hemoglobin levels were checked. We also assessed the neck circumference, dialysis shift, dialysis plan, diabetes history, body mass index (BMI), age, and sex. Results: From a total of 197 patients, 124 cases were men. The mean age of the patients was 54.46 ± 14.84 years. Poor quality of sleep was frequent in 90.86% of the cases. Age, BMI, a history of diabetes mellitus and the product of calcium and phosphorus were independent factors affecting the quality of sleep. Serum calcium and phosphorus levels, hemoglobin, sex, dialysis shift, dialysis plan, neck circumference and dialysis quality showed to have no significant effect on the quality of sleep. Conclusions: Poor quality of sleep is very frequent in patients on maintenance hemodialysis. Further studies are required for better understanding of risk factors associated with the poor quality of sleep to find possible treatments for these patients. Keywords: Hemodialysis; Sleep; Questionnaire; Pittsburgh Sleep Quality Index; Chronic Kidney Disease