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Subfailure damage in ligaments was evaluated macroscopically from a structural perspective (referring to the entire ligament as a structure) and microscopically from a cellular perspective. Freshly harvested rat medial collateral ligaments (MCLs) were used as a model in ex vivo experiments. Ligaments were preloaded with 0.1 N to establish a consistent point of reference for length (and strain) measurements. Ligament structural damage was characterized by nonrecoverable difference in tissue length after a subfailure stretch. The tissue's mechanical properties (via stress vs. strain curves measured from a preloaded state) after a single subfailure stretch were also evaluated (n = 6 pairs with a different stretch magnitude applied to each stretched ligament). Regions containing necrotic cells were used to characterize cellular damage after a single stretch. It should be noted that the number of damaged cells was not quantified and the difference between cellular area and area of fluorescence is not known. Structural and cellular damage were represented and compared as functions of subfailure MCL strains. Statistical analysis indicated that the onset of structural damage occurs at 5.14% strain (referenced from a preloaded length). Subfailure strains above the damage threshold changed the shape of the MCL stress-strain curve by elongating the toe region (i.e., increasing laxity) as well as decreasing the tangential modulus and ultimate stress. Cellular damage was induced at ligament strains significantly below the structural damage threshold. This cellular damage is likely to be part of the natural healing process in mildly sprained ligaments.
Estimating cause‐specific mortality is often of central importance for understanding the dynamics of wildlife populations. Despite such importance, methodology for estimating and analyzing cause‐specific mortality has received little attention in wildlife ecology during the past 20 years. The issue of analyzing cause‐specific, mutually exclusive events in time is not unique to wildlife. In fact, this general problem has received substantial attention in human biomedical applications within the context of biostatistical survival analysis. Here, we consider cause‐specific mortality from a modern biostatistical perspective. This requires carefully defining what we mean by cause‐specific mortality and then providing an appropriate hazard‐based representation as a competing risks problem. This leads to the general solution of cause‐specific mortality as the cumulative incidence function (CIF). We describe the appropriate generalization of the fully nonparametric staggered‐entry Kaplan–Meier survival estimator to cause‐specific mortality via the nonparametric CIF estimator (NPCIFE), which in many situations offers an attractive alternative to the Heisey–Fuller estimator. An advantage of the NPCIFE is that it lends itself readily to risk factors analysis with standard software for Cox proportional hazards model. The competing risks‐based approach also clarifies issues regarding another intuitive but erroneous “cause‐specific mortality” estimator based on the Kaplan–Meier survival estimator and commonly seen in the life sciences literature.
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