Local Orthogonal Rectification: A New Tool for Geometric Phase Space Analysis

Local orthogonal rectification (LOR) provides a natural and useful geometric frame for analyzing dynamics relative to manifolds embedded in flows. LOR can be applied to any embedded base manifold in a system of ODEs of arbitrary dimension to establish a corresponding system of LOR equations for analyzing dynamics within the LOR frame. The LOR equations encode geometric properties of the underlying flow and remain valid, in general, beyond a local neighborhood of the embedded manifold. Additionally, we illustrate the utility of LOR by showing a wide range of application domains. In the plane, we use the LOR approach to derive a novel definition for rivers, long-recognized but poorly understood trajectories that locally attract other orbits yet need not be related to invariant manifolds or other familiar phase space structures, and to identify rivers within several example systems. In higher dimensions, we apply LOR to identify periodic orbits and study the transient dynamics nearby. In the LOR method, %in $\R^n$ for any $n$, the standard approach of finding periodic orbits by solving for fixed points of a Poincar\'{e} return map is replaced by the solution of a boundary value problem with fixed endpoints, and the computation provides information about the stability of the identified orbit. We detail the general method and derive theory to show that once a periodic orbit has been identified with LOR, the LOR coordinate system allows us to characterize the stability of the periodic orbit, to continue the orbit with respect to system parameters, to identify invariant manifolds attendant to the periodic orbit, and to compute the asymptotic phase associated with points in a neighborhood of the periodic orbit in a novel way. Finally, we generalize the definition of rivers beyond planar systems, and demonstrate a fundamental connection between canard solutions in two-timescale systems and generalized rivers. We will again use a blow-up transformation on the LOR equations, which provides a useful decomposition for studying trajectories' behavior relative to the embedded base curve

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Endoprosthetic proximal femur replacement: Metastatic versus primary tumors

Abstract Few studies have examined the impact of underlying diagnosis on the functional and oncologic outcomes following endoprosthetic proximal femur replacement (PFR). We performed a retrospective review of 61 consecutive cemented bipolar PFR in 59 patients for treatment neoplastic lesions with a minimum follow-up of 24 months. Twenty-two patients had primary bone tumors and 39 had metastatic disease. Average follow-up for the 30 surviving patients was 55.4 months and the mean postoperative survival for the 29 patients who died was 12.2 months. Patients with primary tumors demonstrated significantly better functional outcomes than those with metastatic disease, with mean Musculoskeletal Tumor Society functional scores of 80.2 and 66.8%, respectively (p Z 0.0002). Age correlated inversely with functional scores (r Z À0.48; p Z 0.0002), while femoral resection length did not. Preoperative pathologic fracture did not appear to adversely impact final functional outcomes. The KaplaneMeier 5-year implant survival estimate was 92.5%, with aseptic loosening as the endpoint. Both functional results and survival are increased for primary tumors versus metastatic disease following PFR. However, PFR results in excellent local disease control, reliable pain relief and good functional results in both groups, with prosthesis survival exceeding that of the patient in many cases. Published by Elsevier Ltd

Nonmechanical Revision Indications Portend Repeat Limb-Salvage Failure Following Total Femoral Replacement.

BackgroundThere is scant evidence to guide decision-making for patients considering total femoral replacement (TFR). We aimed to identify the indication, patient, disease, and surgical technique-related factors associated with failure. We hypothesized that failure occurs more frequently in the setting of revision surgical procedures, with infection as the predominant failure mode.MethodsWe performed a retrospective cohort study of patients receiving total femoral endoprostheses for oncological and revision arthroplasty indications; 166 patients met these criteria. Our primary independent variable of interest was TFR for a revision indication (arthroplasty or limb salvage); the primary outcome was failure. Analyses were performed for patient variables (age, sex, diagnosis group, indication), implant variables (model, decade, length, materials), and treatment variables. We analyzed TFR failures with respect to patient factors, operative technique, and time to failure. We conducted bivariate logistic regressions predicting failure and used a multivariate model containing variables showing bivariate associations with failure.ResultsForty-four patients (27%) had treatment failure. Failure occurred in 24 (23%) of 105 primary TFRs and in 20 (33%) of 61 revision TFRs; the difference was not significant (p = 0.134) in bivariate analysis but was significant (p = 0.044) in multivariate analysis. The mean age at the time of TFR was 37 years in the primary group and 51 years in the revision group (p = 0.0006). Of the patients who had mechanical failure, none had reoccurrence of their original failure mode, whereas all 8 patients from the nonmechanical cohort had reoccurrence of the original failure mode; this difference was significant (p = 0.0001).ConclusionsTFR has a high failure rate and a propensity for deep infection, especially in the setting of revision indications and prior infection. All failed TFRs performed for revision indications for infection or local recurrence failed by reoccurrence of the original failure mode and resulted in amputation.Level of evidenceTherapeutic Level IV. See Instructions for Authors for a complete description of levels of evidence

Nonmechanical Revision Indications Portend Repeat Limb-Salvage Failure Following Total Femoral Replacement

BackgroundThere is scant evidence to guide decision-making for patients considering total femoral replacement (TFR). We aimed to identify the indication, patient, disease, and surgical technique-related factors associated with failure. We hypothesized that failure occurs more frequently in the setting of revision surgical procedures, with infection as the predominant failure mode.MethodsWe performed a retrospective cohort study of patients receiving total femoral endoprostheses for oncological and revision arthroplasty indications; 166 patients met these criteria. Our primary independent variable of interest was TFR for a revision indication (arthroplasty or limb salvage); the primary outcome was failure. Analyses were performed for patient variables (age, sex, diagnosis group, indication), implant variables (model, decade, length, materials), and treatment variables. We analyzed TFR failures with respect to patient factors, operative technique, and time to failure. We conducted bivariate logistic regressions predicting failure and used a multivariate model containing variables showing bivariate associations with failure.ResultsForty-four patients (27%) had treatment failure. Failure occurred in 24 (23%) of 105 primary TFRs and in 20 (33%) of 61 revision TFRs; the difference was not significant (p = 0.134) in bivariate analysis but was significant (p = 0.044) in multivariate analysis. The mean age at the time of TFR was 37 years in the primary group and 51 years in the revision group (p = 0.0006). Of the patients who had mechanical failure, none had reoccurrence of their original failure mode, whereas all 8 patients from the nonmechanical cohort had reoccurrence of the original failure mode; this difference was significant (p = 0.0001).ConclusionsTFR has a high failure rate and a propensity for deep infection, especially in the setting of revision indications and prior infection. All failed TFRs performed for revision indications for infection or local recurrence failed by reoccurrence of the original failure mode and resulted in amputation.Level of evidenceTherapeutic Level IV. See Instructions for Authors for a complete description of levels of evidence

Stem Cell-based Composite Tissue Constructs for Regenerative Medicine

A major task of contemporary medicine and dentistry is restoration of human tissues and organs lost to diseases and trauma. A decade-long intense effort in tissue engineering has provided the proof of concept for cell-based replacement of a number of individual tissues such as the skin, cartilage, and bone. Recent work in stem cell-based in vivo restoration of multiple tissue phenotypes by composite tissue constructs such as osteochondral and fibro-osseous grafts has demonstrated probable clues for bioengineered replacement of complex anatomical structures consisting of multiple cell lineages such as the synovial joint condyle, tendon-bone complex, bone-ligament junction, and the periodontium. Of greater significance is a tangible contribution by current attempts to restore the structure and function of multitissue structures using cell-based composite tissue constructs to the understanding of ultimate biological restoration of complex organs such as the kidney or liver. The present review focuses on recent advances in stem cell-based composite tissue constructs and attempts to outline challenges for the manipulation of stem cells in tailored biomaterials in alignment with approaches potentially utilizable in regenerative medicine of human tissues and organs. © 2005 Wiley Periodicals, Inc