Fixed Point Indices and Manifolds with Collars

This paper concerns a formula which relates the Lefschetz number L(f) for a map f:M --> M' to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of M. Here M is a compact manifold and M' is M with a collar attached.Comment: Accepted for publication in Fixed Point Theory and Applications as part of the proceedings of the Newfoundland conference on fixed points, 200

Factors That Predict Short-term Complication Rates After Total Hip Arthroplasty

Background: There remains uncertainty regarding the relative importance of patient factors such as comorbidity and provider factors such as hospital volume in predicting complication rates after total hip arthroplasty (THA). Purpose: We therefore identified patient and provider factors predicting complications after THA. Methods: We reviewed discharge data from 138,399 patients undergoing primary THA in California from 1995 to 2005. The rate of complications during the first 90 days postoperatively (mortality, infection, dislocation, revision, perioperative fracture, neurologic injury, and thromboembolic disease) was regressed against a variety of independent variables, including patient factors (age, gender, race/ethnicity, income, Charlson comorbidity score) and provider variables (hospital volume, teaching status, rural location). Results: Compared with patients treated at high-volume hospitals (above the 20th percentile), patients treated at low-volume hospitals (below the 60th percentile) had a higher aggregate risk of having short-term complications (odds ratio, 2.00). A variety of patient factors also had associations with an increased risk of complications: increased Charlson comorbidity score, diabetes, rheumatoid arthritis, advanced age, male gender, and black race. Hispanic and Asian patients had lower risks of complications. Conclusions: Patient and provider characteristics affected the risk of a short-term complication after THA. These results may be useful for educating patients and anticipating perioperative risks of THA in different patient populations. Level of Evidence: Level II, prognostic study. See Guidelines for Authors for a complete description of levels of evidence. © 2010 The Author(s)

Inter- and intra-observer reliability of the Baumann angle of the humerus in children with supracondylar humeral fractures

The Baumann angle of the humerus has been commonly used as an outcome measure for supracondylar fractures in children. However, there is limited or no information about the reliability of this measurement. The purpose of this study was to determine the inter-observer reliability (IEOR) and intra-observer reliability (IAOR) of the Baumann angle of the humerus. The Baumann angle of the humerus was measured by five observers on the anteroposterior radiographs of 35 children’s elbows, all of which had sustained a nondisplaced supracondylar humeral fracture. The values of IEOR and IAOR were calculated using a Pearson coefficient of correlation. Ranges of differences in the measurement of the Baumann angle of the humerus were established, and the percentage of agreement between observers was then calculated using those ranges. The Baumann angle of the humerus is a simple, repeatable and reliable measurement that can be used for the determination of the outcome of supracondylar humeral fractures in the paediatric population. An excellent IEOR was found for the measurement of the Baumann angle (r = 0.78, p = 0.0001). When the difference between observers in the reported measurement of the Baumann’s angle was calculated to be within seven degrees of each other, at least four of the five observers agreed 100% of the time. Similarly, excellent values of IAOR were found for the measurement of the Baumann’s angle (r = 0.80, p = 0.0001). Level of evidence for this study was III

Combined use of bFGF and GDF-5 enhances the healing of medial collateral ligament injury

Basic fibroblast growth factor (bFGF) and growth and differentiation factor (GDF)-5 stimulate the healing of medial collateral ligament (MCL) injury. However, the effect of isolated and combined use of bFGF/GDF-5 remains still unclear. We investigated cellular proliferation and migration responding to bFGF/GDF-5 using rabbit MCL fibroblasts. Rabbit MCL injury was treated by bFGF and/or GDF-5 with peptide hydrogels. Gene expression and deposition of collagens in healing tissues were evaluated. bFGF/GDF-5 treatment additively enhanced cell proliferation and migration. bFGF/GDF-5 hydrogels stimulated Col1a1 expression without increasing Col3a1 expression. Combined use of bFGF/GDF-5 stimulated type I collagen deposition and the reorganization of fiber alignment, and induced better morphology of fibroblasts in healing MCLs. Our study indicates that combined use of bFGF/GDF-5 might enhance MCL healing by increasing proliferation and migration of MCL fibroblasts, and by regulating collagen synthesis and connective fiber alignment

The effects of thermal capsulorrhaphy of medial parapatellar capsule on patellar lateral displacement

<p>Abstract</p> <p>Background</p> <p>The effectiveness of thermal shrinkage on the medial parapatellar capsule for treating recurrent patellar dislocation is controversial. One of reasons why it is still controversial is that the effectiveness is still qualitatively measured. The purpose of this study was to quantitatively determine the immediate effectiveness of the medial parapatellar capsule shrinkage as in clinical setting.</p> <p>Methods</p> <p>Nine cadaveric knees were used to collect lateral displacement data before and after medial shrinkage or open surgery. The force and displacement were recorded while a physician pressed the patella from the medial side to mimic the physical exam used in clinic. Ten healthy subjects were used to test the feasibility of the technique on patients and establish normal range of lateral displacement of the patella under a medial force. The force applied, the resulting displacement and the ratio of force over displacement were compared among four data groups (normal knees, cadaveric knees before medial shrinkage, after shrinkage and after open surgery).</p> <p>Results</p> <p>Displacements of the cadaveric knees both before and after thermal modification were similar to normal subjects, and the applied forces were significantly higher. No significant differences were found between before and after thermal modification groups. After open surgery, displacements were reduced significantly while applied forces were significantly higher.</p> <p>Conclusion</p> <p>No immediate difference was found after thermal shrinkage of the medial parapatellar capsule. Open surgery immediately improved of the lateral stiffness of the knee capsule.</p

Fixed point indices, transfers and path fields

Let $V$ be a vector field on a compact differentiable manifold $M$. Assume $V$ has no zeros on the boundary $\partial M$. Marston Morse discovered in 1929 an interesting formula relating the indices of the vector field $V$ and of a vector field $\partial\underline{\enspace} V$ defined on a part of the boundary to the Euler characteristic of $M:{\rm Ind}(V) + {\rm Ind} (\partial\underline{\enspace} V)$ = $\chi(M)$; this formula generalizes the well-known Poincare-Hopf Index Theorem for vector fields. In this work we obtain analogous formulas, $I(f)$ + I(rf\vert\sb{\partial\underline{\enspace} M} = $\chi(M)$ for fixed point indices, t\sb{rf} = t\sb{f}\ \circ\ \breve i\sbsp{1}{\*}+t\sb{\partial\underline{\enspace} f}\ \circ\ \breve i\sp{\*}\ \circ\ \breve i\sbsp{2}{\*} for fixed point transfers and Ind($\sigma$) + Ind($\partial\underline{\enspace}\sigma$) = $\chi(M)$ for path field indices