Anterior shear strength of the porcine lumbar spine after laminectomy and partial facetectomy

Degenerative lumbar spinal stenosis is the most common reason for lumbar surgery in patients in the age of 65 years and older. The standard surgical management is decompression of the spinal canal by laminectomy and partial facetectomy. The effect of this procedure on the shear strength of the spine has not yet been investigated in vitro. In the present study we determined the ultimate shear force to failure, the displacement and the shear stiffness after performing a laminectomy and a partial facetectomy. Eight lumbar spines of domestic pigs (7 months old) were sectioned to obtain eight L2–L3 and eight L4–L5 motion segments. All segments were loaded with a compression force of 1,600 N. In half of the 16 motion segments a laminectomy and a 50% partial facetectomy were applied. The median ultimate shear force to failure with laminectomy and partial facetectomy was 1,645 N (range 1,066–1,985) which was significantly smaller (p = 0.012) than the ultimate shear force to failure of the control segments (median 2,113, range 1,338–2,659). The median shear stiffness was 197.4 N/mm (range 119.2–216.7) with laminectomy and partial facetectomy which was significantly (p = 0.036) smaller than the stiffness of the control specimens (median 216.5, 188.1–250.2). It was concluded that laminectomy and partial facetectomy resulted in 22% reduction in ultimate shear force to failure and 9% reduction in shear stiffness. Although relatively small, these effects may explain why patients have an increased risk of sustaining shear force related vertebral fractures after spinal decompression surgery

Convergent meshfree approximation schemes of arbitrary order and smoothness

Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order one, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space W^(1,p), i.e., they are C^0-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in W^(k,p), i.e., they are C^k-continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev space W^(k,p), for any 1⩽p<∞. The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised

HOLMES: Convergent Meshfree Approximation Schemes of Arbitrary Order and Smoothness

Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order 1, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space W^(1,p), i.e., they are C⁰-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in W^(k,p), i.e., they are C^k -continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev Space W^(k,p), for any 1 ≤ p < ∞. The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised