Abstract. In this paper, we define the normalized L p intersection body and prove that the normalized L p intersection body operator is GL(n) contravariant of weight 0 . We show that the polar body operator can be obtained as a limit of the normalized L p intersection body operator. And we establish a dual Brunn-Minkowski type inequality for normalized L p intersection bodies. Furthermore, the normalized L p -Busemann-Petty problem is shown.Mathematics subject classification (2010): 52A40, 53A15.
Objective: To investigate the clinical value of peripheral blood lymphocytes immunophenotyping and Natural Killer cells (NK) in the judgment of the types of Connective Tissue Disease Combined with Interstitial Lung Disease (CTD-ILD). Methods: 262 CTD-ILD patients and 50 healthy volunteers in our hospital from January 2010 to December 2015 were enrolled into the study. There were 164 patients with CTD-ILD and 98 patients with ILD. The clinical symptoms and High Resolution CT (HRCT) of all patients were observed and compared between the two groups. The serum levels of CD3 + , CD4 + , CD8 + , CD19 + , CD56 + T cells were detected by flow cytometry and compared among the three groups. Results: There were no difference of the clinical symptoms and the characteristics of HRCT between the two patients groups (P>0.05). The serum level of CD3 +-CD8 + T cells of patients in the CTD-ILD group was higher than the control group and ILD group (P<0.05); and the serum level of CD3-CD56 + T cells and the ratio of CD4 + /CD8 + in the CTD-ILD group was lower than the control group and ILD group (P<0.05). But there was no difference of the peripheral blood lymphocytes immunophenotyping between the ILD group and control group (P>0.05). Conclusion: The immunophenotype of peripheral blood lymphocytes could be helpful to judge the types of connective tissue disease combined with interstitial lung disease.
Objective: To investigate the clinical value of peripheral serum levels of Surfactant Protein D (SP-D), anti-melanoma differentiation-associated gene 5 (MDA5), Insulation (IL-6) and Tumor Necrosis Factor (TNF-α) in the prognosis of the degree of Connective Tissue Disease combined with Interstitial Lung Disease (CTD-ILD). Methods: 339 CTD-ILD patients, 184 CTD patients and 64 healthy volunteers in our hospital from January 2010 to December 2015 were enrolled into the study. The clinical symptoms, the test of High Resolution CT (HRCT) and lung function of all patients were detected and compared between the CTD-ILD and CTD patients. The serum levels of SP-D, anti-MDA5, IL-6, TNF-α were detected by ELISA among the three groups. Results: The mean serum levels of SP-D, anti-MDA5, IL-6, TNF-α of CTD-ILD patients and CTD patients were both higher than the control group (P<0.05); and the mean serum levels of SP-D, anti-MDA5, IL-6 of CTD-ILD patients was higher than CTD patients (P<0.05). The mean level of SP-D of CTD-ILD patients with pant was higher than the patients without pant (P<0.05); the mean level of anti MDA5 of CTD-ILD patients with rash was higher than the patients without rash (P<0.05); the mean level of TNF-α of CTD-ILD patients with atony or cough was higher than the patients without atony or cough (P<0.05). The serum levels of SP-D, anti-MDA5, IL-6, TNF-α in CTD-ILD patients were related to the degree of pulmonary ventilation disorder and pulmonary diffuse dysfunction. Conclusion: The detection of SP-D, anti-MDA5, IL-6, TNF-α of CTD-ILD patients could be helpful to diagnose the degree of connective tissue disease combined with interstitial lung disease.
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