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In this article, we investigate F -pure thresholds of polynomials that are homogeneous under some N-grading, and have an isolated singularity at the origin. We characterize these invariants in terms of the base p expansion of the corresponding log canonical threshold. As an application, we are able to make precise some bounds on the difference between F -pure and log canonical thresholds established by Mustaţȃ and the fourth author. We also examine the set of primes for which the F -pure and log canonical threshold of a polynomial must differ. Moreover, we obtain results in special cases on the ACC conjecture for F -pure thresholds, and on the upper semi-continuity property for the F -pure threshold function.

The material properties of tendon type I collagen fibers polymerized with nordihydroguaiaretic acid (NDGA) are equivalent to native tendon, suggesting that NDGA crosslinking may provide a viable approach to stabilizing collagenous materials for repairing ruptured, lacerated, or surgically transected fibrous tissues, such as tendon and ligament (Koob & Hernandez, Biomaterials, in press). Using standard cytotoxicity tests, the present study evaluated the biocompatibility of these fibers with cultured bovine tendon fibroblasts. Primary fibroblasts obtained from calf digital extensor tendons were exposed to NDGA, reaction products generated from the polymerization protocol, and the crosslinked fibers. NDGA was cytotoxic to these cells at concentrations above 100 microM. NDGA oxidation products were similarly cytotoxic. At concentrations below 100 microM, fibroblast viability was not affected by NDGA or its oxidation products. At these lower concentrations, fibroblast proliferation was unaffected compared to controls not exposed to NDGA. Fibers crosslinked with NDGA contained no unreacted NDGA, but they did contain soluble reaction products that were cytotoxic to tendon fibroblasts in both the elution and the direct contact tests. Washing the fibers in 70% ethanol and phosphate-buffered saline eliminated cytotoxicity of the fibers. Ethanol simultaneously sterilized the fibers. Tensile tests established that the ethanol/phosphate buffer wash did not adversely affect the material properties of the fibers. The results of these experiments indicate that NDGA-crosslinked fibers can be rendered nontoxic to tendon fibroblasts and may provide a novel approach for producing biologically based, biocompatible, tendon bioprostheses.

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