181 research outputs found

    Lower bounds on the dilation of plane spanners

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    (I) We exhibit a set of 23 points in the plane that has dilation at least 1.43081.4308, improving the previously best lower bound of 1.41611.4161 for the worst-case dilation of plane spanners. (II) For every integer n13n\geq13, there exists an nn-element point set SS such that the degree 3 dilation of SS denoted by δ0(S,3) equals 1+3=2.7321\delta_0(S,3) \text{ equals } 1+\sqrt{3}=2.7321\ldots in the domain of plane geometric spanners. In the same domain, we show that for every integer n6n\geq6, there exists a an nn-element point set SS such that the degree 4 dilation of SS denoted by δ0(S,4) equals 1+(55)/2=2.1755\delta_0(S,4) \text{ equals } 1 + \sqrt{(5-\sqrt{5})/2}=2.1755\ldots The previous best lower bound of 1.41611.4161 holds for any degree. (III) For every integer n6n\geq6 , there exists an nn-element point set SS such that the stretch factor of the greedy triangulation of SS is at least 2.02682.0268.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2 table

    Intra-arterial peptide-receptor radionuclide therapy for neuro-endocrine tumour liver metastases:an in-patient randomised controlled trial (LUTIA)

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    Purpose: Peptide receptor radionuclide therapy (PRRT) using [177Lu]Lu-DOTATATE has been shown to effectively prolong progression free survival in grade 1–2 gastroenteropancreatic neuroendocrine tumours (GEP-NET), but is less efficacious in patients with extensive liver metastases. The aim was to investigate whether tumour uptake in liver metastases can be enhanced by intra-arterial administration of [177Lu]Lu-DOTATATE into the hepatic artery, in order to improve tumour response without increasing toxicity. Methods: Twenty-seven patients with grade 1–2 GEP-NET, and bi-lobar liver metastases were randomized to receive intra-arterial PRRT in the left or right liver lobe for four consecutive cycles. The contralateral liver lobe and extrahepatic disease were treated via a “second-pass” effect and the contralateral lobe was used as the control lobe. Up to three metastases (&gt; 3 cm) per liver lobe were identified as target lesions at baseline on contrast-enhanced CT. The primary endpoint was the tumour-to-non-tumour (T/N) uptake ratio on the 24 h post-treatment [177Lu]Lu-SPECT/CT after the first cycle. This was calculated for each target lesion in both lobes using the mean uptake. T/N ratios in both lobes were compared using paired-samples t-test. Findings: After the first cycle, a non-significant difference in T/N uptake ratio was observed: T/NIA = 17·4 vs. T/Ncontrol = 16·2 (p = 0·299). The mean increase in T/N was 17% (1·17; 95% CI [1·00; 1·37]). Of all patients, 67% (18/27) showed any increase in T/N ratio after the first cycle. Conclusion: Intra-arterial [177Lu]Lu-DOTATATE is safe, but does not lead to a clinically significant increase in tumour uptake.</p
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