Purpose To verify whether femoral anteversion measured by the surgical transepicondylar axis (S-FA) is a reliable parameter for evaluating femoral rotational deformities and to provide an indication for derotational distal femoral osteotomy (DDFO) in patients with patellar dislocation. Methods Ninety patients with recurrent patellar dislocation and 90 healthy individuals were enrolled. The S-FA, the femoral anteversion measured by posterior condylar reference line (P-FA), the length of posterior femoral condyles, and the posterior condylar angle (PCA) were assessed by CT images. The unpaired t test and Pearson correlation analysis were conducted. Receiver operating characteristic curves and the area under the curve (AUC) were used to evaluate the diagnostic capacity of the parameters. The pathological value of the measurements was determined, and a binary regression model was established. Results The S-FA and P-FA were greater in the study group (14.2 ± 7.7° and 19.7 ± 7.3°, respectively) than in the control group (7.2 ± 8.0° and 12.2 ± 8.2°, respectively) (P < 0.001). The lateral/posterior condyle was shorter in patients with patellar dislocation (21.2 ± 2.5 mm) than in healthy individuals (23.5 ± 2.7 mm) (P = 0.001). The P-FA was correlated with PCA in the study group (P < 0.001). The S-FA and P-FA had AUCs of 0.734 and 0.767 for patellar dislocation, respectively. The pathological values of the S-FA and P-FA were 20.4° and 25.8°, respectively. The S-FA revealed a signiicant OR of 10.47 (P = 0.014) for patellar dislocation. ConclusionThe S-FA is a reliable parameter for identifying femoral rotational deformities in patients with patellar dislocation. DDFO is recommended when a pathological S-FA (> 20.4°) is presented. Level of evidence Retrospective cohort study (diagnostic), level II.

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

Circulant and skew circulant matrices have become an important tool in networks engineering. In this paper, we consider skew circulant type matrices with any continuous Fibonacci numbers. We discuss the invertibility of the skew circulant type matrices and present explicit determinants and inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

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