In this retrospective study, we randomly selected 60 MRIs (39 women and 21 men) of the lumbar region from a sample of a large cohort study, which was approved by the local ethics committee (EA1/058/21). MRI scans were conducted using a Siemens Avanto 1.5 T MRI system (Siemens AG, Erlangen, Germany) with T2-weighted turbo spin echo sequences for both axial and sagittal images. The axial T2 parameters used were a repetition time of 4.000, an echo time of 113, and a slice thickness of 3 mm. As the vast majority of degenerative changes can be detected in the lower spine, the levels L4–L5 and L5-S1 were evaluated.

All measurements were performed by two orthopedic residents, who were trained in the MRI muscle assessment. The MRI images were measured through the two different image processing programs (ImageJ and Amira). The two observers measured the MRIs in a random order for both investigators. The CSA of the multifidus muscle (MF) and erector spinae muscle (ES) was measured at mid-disk level L4/5 and L5/S1 (Fig. 1), the CSA was single measured before applying any thresholds. FCSA and FCSA/CSA were determined using two different segmentation thresholds for differentiating muscle fibers and fatty muscle infiltration.

L5/S1 MRI of the same subject, A and B are processed by ImageJ, C and D by Amira

Circle method: Six regions of interest (ROIs) from the muscles of the MF and ES were taken from the visible areas of muscle tissue with least visual fatty infiltration. The maximum value that can be obtained from a sample ROI is regarded as the upper threshold to distinguish between muscle tissue and fat. Since the lower limit is usually 0 or close to 0, uniformly setting the lower limit at 0 is used to minimize errors (defined as Circle method) [14].

Overlap method: Outline CSA of paraspinal muscle (include ES and MF) and subcutaneous fat (SC) on both sides. By presenting the grayscale ranges for both CSA and SC as histograms and overlaying them, it was possible to identify signal intensities that were common to both images. The Overlapping area of the histograms represents the intensity of the fatty signal in the CSA (defined as Overlap method) [15].

For each measurement, descriptive statistics such as means \((\overline x)\) and standard deviations (SD) were calculated. The inter-rater, inter-software, and inter-threshold reliability of the measurement were evaluated using intra-class correlation coefficient (ICC). Agreement was defined according to Portney and Watkins [16]: an ICC of 0.00–0.49 is considered poor, 0.50–0.74 is moderate, and 0.75–1.0 is excellent. As Bland and Altman suggested [17, 18], the 95% limits of agreement were used to evaluate the agreement between the measurements acquired by different raters using different software with different thresholds. The standard error of measurement (SEM) is a statistical metric used to estimate the expected error associated with a specific measurement \(\left( } = S\sqrt } \right)\), where S is the standard deviation of the test and rxx represents the reliability of the test. In this study, the results were analyzed based on the muscles and spinal level that were investigated. The Wilcoxon Rank Sum Test is employed to analyze systematic differences between different thresholds. The statistical analysis was conducted using Statistical Package for the Social Sciences version 23.0 (SPSS Inc, Chicago, Illinois).

Based on Cohen’s suggestions [19], By utilizing G*Power version 3.1.3 (University of Düsseldorf, Düsseldorf, Germany), effect size conventions were provided in categories of “small,” “medium,” and “large” to determine the required sample size. In this study, with an effect size of 0.3, alpha error of 0.05, and a power (verification) of 0.8, the minimum sample size of 46 participants was determined. Therefore, the enrollment of 60 patients was considered adequate to achieve the desired statistical power.