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We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities.

SUMMARYWe present the Bézier extraction operator and isogeometric Bézier elements for non-uniform rational BSpline (NURBS)-based isogeometric analysis. The Bézier extraction operator allows numerical integration of smooth functions to be performed on C 0 Bézier elements. We show how the Bézier extraction operator is computed for NURBS. We then show that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays. All significant changes may be implemented in a shape function subroutine.

SummaryBackgroundMore than half of patients with multiple sclerosis have progressive disease characterised by accumulating disability. The absence of treatments for progressive multiple sclerosis represents a major unmet clinical need. On the basis of evidence that mesenchymal stem cells have a beneficial effect in acute and chronic animal models of multiple sclerosis, we aimed to assess the safety and efficacy of these cells as a potential neuroprotective treatment for secondary progressive multiple sclerosis.MethodsPatients with secondary progressive multiple sclerosis involving the visual pathways (expanded disability status score 5·5–6·5) were recruited from the East Anglia and north London regions of the UK. Participants received intravenous infusion of autologous bone-marrow-derived mesenchymal stem cells in this open-label study. Our primary objective was to assess feasibility and safety; we compared adverse events from up to 20 months before treatment until up to 10 months after the infusion. As a secondary objective, we chose efficacy outcomes to assess the anterior visual pathway as a model of wider disease. Masked endpoint analyses was used for electrophysiological and selected imaging outcomes. We used piecewise linear mixed models to assess the change in gradients over time at the point of intervention. This trial is registered with ClinicalTrials.gov, number NCT00395200.FindingsWe isolated, expanded, characterised, and administered mesenchymal stem cells in ten patients. The mean dose was 1·6×106 cells per kg bodyweight (range 1·1–2·0). One patient developed a transient rash shortly after treatment; two patients had self-limiting bacterial infections 3–4 weeks after treatment. We did not identify any serious adverse events. We noted improvement after treatment in visual acuity (difference in monthly rates of change −0·02 logMAR units, 95% CI −0·03 to −0·01; p=0·003) and visual evoked response latency (−1·33 ms, −2·44 to −0·21; p=0·020), with an increase in optic nerve area (difference in monthly rates of change 0·13 mm2, 0·04 to 0·22; p=0·006). We did not identify any significant effects on colour vision, visual fields, macular volume, retinal nerve fibre layer thickness, or optic nerve magnetisation transfer ratio.InterpretationAutologous mesenchymal stem cells were safely given to patients with secondary progressive multiple sclerosis in our study. The evidence of structural, functional, and physiological improvement after treatment in some visual endpoints is suggestive of neuroprotection.FundingMedical Research Council, Multiple Sclerosis Society of Great Britain and Northern Ireland, Evelyn Trust, NHS National Institute for Health Research, Cambridge and UCLH Biomedical Research Centres, Wellcome Trust, Raymond and Beverly Sackler Foundation, and Sir David and Isobel Walker Trust.

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