Question E (7) of the 2023 China Graduate Mathematical Modeling Competition: Question 2a: Research on the correlation between modeling and treatment of edema around hematoma (theoretical part)

1. Analysis of question 2a

This problem involves constructing a curve of progression of edema volume over time and calculating the residual between the true value and the fitted curve.

We first need to obtain the edema volume data of the first 100 patients from the attached data, as well as the relevant repeated examination time points and their corresponding indicators. Our goal is to create a curve where the axis represents the time interval from onset to imaging time and the axis represents edema volume.

In order to understand the trend of edema volume over time, we first need to draw a scatter plot. The abscissa represents the time interval from onset to imaging examination, and the ordinate represents the edema volume. Each scatter point represents an observation for one patient. By observing the scatter plot, we can get a preliminary understanding of the distribution of the data. This includes the range of changes in edema volume and whether there are obvious trends or patterns. For example, we can check if there is an increasing or decreasing trend, or if there are outliers.

We need to choose the appropriate