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The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

ABSTRACT: BACKGROUND AND AIMS:In some dicotyledonous leaves and leaflets, the secondary veins run more-or-less straight to the margins and have well-defined lengths. For a given half-lamina of length L, an equation, previously proposed, relates the lengths of these veins, p, to the distances, l, between the leaf tip and their insertions on the midrib: p = B2(x+y)l(x)(L - l)(y)/L(x+y-1), where B, x and y are fitted parameters. Aspects of the formula are re-examined, including its general applicability, significance and usefulness. METHODS:Length measurements were made on leaves of various dicotyledons, notably Ulmus glabra, U. procera, Alnus viridis, A. glutinosa, Corylus avellana and Crataegus monogyna. Equations were fitted by non-linear regression. KEY RESULTS:The equation has now been applied descriptively to 23 species of eight families, but it is sometimes preferable or necessary to replace the measured length, L, with a fourth parameter that may differ significantly from it. Within a given species, values of the indices x and y are positively correlated. Leaves of some U. glabra depart qualitatively from the general pattern. As an example of hypothesis testing, the equation was used to show that the retuse or emarginate leaf tips of A. glutinosa are not due to stunting. CONCLUSIONS; That the equation applies to many species suggests that the underlying processes of leaf growth are quantitatively similar. Although relevant knowledge of these is scant, consideration of mathematical relationships may help their elucidation.

SUBMITTER: Burton RF

PROVIDER: S-EPMC4241078 | biostudies-other | 2004 Feb

REPOSITORIES: biostudies-other

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The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

Burton Richard F RF

Annals of botany 20040105 2

<h4>Background and aims</h4>In some dicotyledonous leaves and leaflets, the secondary veins run more-or-less straight to the margins and have well-defined lengths. For a given half-lamina of length L, an equation, previously proposed, relates the lengths of these veins, p, to the distances, l, between the leaf tip and their insertions on the midrib: p = B2(x+y)l(x)(L - l)(y)/L(x+y-1), where B, x and y are fitted parameters. Aspects of the formula are re-examined, including its general applicabil ...[more]

PMID: 14707000

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Project description:ObjectiveTo indirectly compare aflibercept, bevacizumab, dexamethasone, ranibizumab and triamcinolone for treatment of macular oedema secondary to central retinal vein occlusion using a network meta-analysis (NMA).Design nma data sourcesThe following databases were searched from January 2005 to March 2013: MEDLINE, MEDLINE In-process, EMBASE; CDSR, DARE, HTA, NHSEED, CENTRAL; Science Citation Index and Conference Proceedings Citation Index-Science.Eligibility criteria for selecting studiesOnly randomised controlled trials assessing patients with macular oedema secondary to central retinal vein occlusion were included. Studies had to report either proportions of patients gaining ?3 lines, losing ?3 lines, or the mean change in best corrected visual acuity. Two authors screened titles and abstracts, extracted data and undertook risk of bias assessment. Bayesian NMA was used to compare the different interventions.ResultsSeven studies, assessing five drugs, were judged to be sufficiently comparable for inclusion in the NMA. For the proportions of patients gaining ?3 lines, triamcinolone 4?mg, ranibizumab 0.5?mg, bevacizumab 1.25?mg and aflibercept 2?mg had a higher probability of being more effective than sham and dexamethasone. A smaller proportion of patients treated with triamcinolone 4?mg, ranibizumab 0.5?mg or aflibercept 2?mg lost ?3 lines of vision compared to those treated with sham. Patients treated with triamcinolone 4?mg, ranibizumab 0.5?mg, bevacizumab 1.25?mg and aflibercept 2?mg had a higher probability of improvement in the mean best corrected visual acuity compared to those treated with sham injections.ConclusionsWe found no evidence of differences between ranibizumab, aflibercept, bevacizumab and triamcinolone for improving vision. The antivascular endothelial growth factors (VEGFs) are likely to be favoured because they are not associated with steroid-induced cataract formation. Aflibercept may be preferred by clinicians because it might require fewer injections.Systematic review registrationNot registered.

Dataset Information

The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

Publications

The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

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