ASSOCIATION OF PECTORALIS MINOR MUSCLE LENGTH AND SHOULDER RANGE OF MOTION AMONG INDIVIDUALS WITH AND WITH OUT SHOULDER PAIN

Background and Aim: To evaluate the association of pectoralis minor muscle length and the shoulder range of motion with and without shoulder pain. Methodology: A sample of 214 participants with and without shoulder pain were enrolled in an analytical cross sectional study at Institute of physical medicine and rehabilitation, Dow University of health sciences, Karachi.  Questionnaire was provided to all participants after taking consent. Individuals were categorized into two equal groups i.e. one with and the other without pain). Shoulder active ranges were measured with universal goniometer and pectoralis minor length with measuring tape. Statistical Package of Social Sciences version 21 was used for data analysis. The descriptive variables were assessed for frequencies and percentages. Continuous variables were shown with mean and standard deviations and were correlated with bivariate correlation test. Considered significant was 0.05 p value. Results: Females were 176(82.2%) and males were 38 (17.8%). Mean ± SD of age, weight, height, and BMI were 26.82 ±7.50, 58.45 ±12.11, 160.59 ± 12.43, and 22.18 ±3.78 respectively. The pain intensity negatively correlated with shoulder range of motions (rs = -0.307 to -0.775, p< 0.05) except medial rotation.  Significant difference (p< 0.05) is found for length of pectoralis minor and range of motion between groups. There was also weak positive correlation between pectoralis minor index and shoulder lateral rotation (rs =0.215; p = 0.003). Conclusion: The shoulder pain affects shoulder joint range of motion and pectoralis minor length. Decreased pectoralis minor muscle length accompanies limited shoulder range of motion except, medial rotation.

Functor and categorical representation of Polylogarithmic groups

In this dissertation we study Polylogarithmic groups in the language of category and functors. By treating Grassmannian complex (simplicial chain complex), Tangential version of Bloch-Suslin complex over ring of dual number for weight 2, 3 and generally n , as the category of Abelian groups and defining functors from one category to another category or one structure to another structure by checking its validation and properties