Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.

Solving surface structures from normal incidence X-ray standing wave data

A program is provided to determine structural parameters of atoms in or adsorbed on surfaces by refinement of atomistic models towards experimentally determined data generated by the normal incidence X-ray standing wave (NIXSW) technique. The method employs a combination of Differential Evolution Genetic Algorithms and Steepest Descent Line Minimisations to provide a fast, reliable and user friendly tool for experimentalists to interpret complex multidimensional NIXSW data sets.

The influence of dietary fatty acid composition on N-ethyl-Nnitrosourea-induced mammary tumour incidence in the rat and on the composition of inositol- and ethanolamine-phospholipids of normal and tumour mammary tissue

This study has investigated the influence of dietary fatty acid composition on mammary tumour incidence in N-ethyl-N-nitrosourea (ENU)-treated rats and has compared the susceptibility to dietary fatty acid modification of the membrane phospholipids phosphatidyliuositol (PI) and phosphatidylethanolamine (PE) from normal and tumour tissue of rat mammary gland. The incidence of mammary tumours was significantly lower in fish oil- (29%), compared with olive oil- (75%; P < 0.04) but not maize oil- (63%; P < 0.1) fed animals. No differences in PI fatty acid composition were found in normal or tumour tissue between rats fed on maize oil, olive oil or fish oil in diets from weaning. When normal and tumour tissue PI fatty acids were compared, significantly higher amounts of stearic acid (18:O) were found in tumour than normal tissue in rats given olive oil (P < 0.05). A similar trend was found in animals fed on maize oil, although differences between normal and tumour tissue did not reach a level of statistical significance (P < 0.1). In mammary PE, maize oil-fed control animals had significantly higher levels of linoleic acid (18:2n-6) than either olive oil- or fish oil-fed animals (P < 0.05, both cases) and levels of arachidonic acid were also higher in maize oil- compared with fish oil-fed animals (P < 0.05). In tumourbearing animals no differences in PE fatty acid composition were found between the three dietary groups. When normal and tumour tissue PE fatty acids were compared, significantly lower amounts of liuoleic acid (18:2n-6; P < 0.01) and significantly greater amounts of arachidonic acid (20:4n-6; P < 0.05) were found in tumour than normal tissue of rats fed on maize oil. The present study shows that the fatty acid composition of PI from both normal and tumour tissue of the mammary gland is resistant to dietary fatty acid modification. The PE fraction is more susceptible to dietary modification and in this fraction there is evidence of increased conversion of linoleic acid to arachidonic acid in tumour compared with normal tissue. Lower tumour incidence rates in rats given fish oils may in part be due to alteration in prostanoid metabolism secondary to displacement of arachidonic acid by eicosapentaenoic acid, but PE rather than PI would appear to be the most likely locus for diet-induced alteration in prostanoid synthesis in this tissue. Effects of dietary fatty acids other than on the balance of n-6 and n-3 fatty acids, and on prostanoid metabolism, should also be considered. The significance of increased stearic acid content of PI in tumours of olive oil-fed animals and the possible influence of dietary fatty acids on the capacity for stearic acid accumulation requires further study.

The effect of triacylglycerol fatty acid positional distribution on postprandial plasma metabolite and hormone responses in normal adult men

The present study has examined the possibility that the positional distribution of fatty acids on dietary triacyglycerol (TAG) influences the postprandial response to a liquid meal in adult subjects. Postprandial TAG, non-esterified fatty acids (NEFA), ketones, glucose, insulin and gastric inhibitory polypeptide (GIP) responses were monitored in sixteen normal adult male subjects over 6 h following consumption of test meals containing dietary TAG in which palmitic acid was predominantly on the sn-1 (Control) or sn-2 positions (Betapol). Plasma total TAG, chylomicron-rich TAG and chylomicron-poor TAG concentrations were identical in response to the two test meals. The peak increase (mean (SD)) in chylomicron TAG was 0.85 (0.46) mmol/l after the Control meal and 0.85 (0.42) mmol/l after the Betapol meal. Plasma glucose, insulin, GIP, NEFA and ketone concentrations were also very similar following the two meals. It is concluded that dietary TAG containing saturated fatty acids on the sn-2 position appear in plasma at a similar level and over a similar timescale to TAG in which saturated fatty acids are predominantly located on sn-1 or sn-3 positions. The results reported in the present study demonstrate that the positional distribution of fatty acids on dietary TAG is not an important determinant of postprandial lipaemia in adult male subjects, but do not exclude the possibility that different responses may occur when these dietary TAG are given long term.

Fatty acid compositions of inositol and choline phospholipids of breast tumours and normal breast tissue

The fatty acid compositions of the -choline and -inositol phospholipids of breast tumours of women undergoing surgery for treatment of breast disease (malignant n = 12; benign n = 10) and normal breast tissue of women undergoing breast reduction surgery (n = 6) were determined. The fatty acid compositions of erythrocyte phospholipids were also determined in the same subjects and in an additional number of normal healthy volunteers (n = 16). Levels of oleic acid were lower in both phospholipid fractions of erythrocytes of women with breast disease and in the phosphatidylcholine fraction of breast tumours compared with normal breast tissue. Significantly higher levels of linoleic acid were found in erythrocytes of tumour-bearing subjects and a similar trend was evident in the phosphatidylcholine fraction of tumour compared with normal breast tissues. Conversely, lower levels of two of the products of linoleic acid chain elongation and desaturation, dihomogamma-linolenic and arachidonic acids, were found in the erythrocyte phospholipids of tumour-bearing subjects and in the choline phospholipids of breast tumour tissues. These data suggest that in women with breast disease, there may be inhibition of 6-desaturase, and enhanced activity of 9-desaturase, enzymes which play an important role in determining membrane phospholipid fatty acid composition. This pattern of altered fatty acid composition characteristic of erythrocyte phospholipids of tumour-bearing subjects and phosphatidylcholine of breast tumour tissue was less evident in the case of the breast tumour phosphatidylinositol in which differences other than those described were seen.

Effects of n-3 fatty acids on postprandial triacylglycerol and hormone concentrations in normal subjects

The present study reports results from two investigations to determine effects of a 6-week period of moderate n-3 fatty acid supplementation (2.7 g/d) on fasting and on postprandial triacylglycerol and metabolic hormone concentrations in response to standard test meals. In the first study postprandial responses were followed for 210 min after an early morning test meal challenge; in the second study responses to an evening test meal were followed during the evening and overnight for a total period of 12 h. In both studies postprandial triacylglycerol responses to the test meals were significantly reduced after compared with before fish-oil supplementation. In the second study the triacylglycerol peak response seen between 200 and 400 min in subjects studied before supplementation with fish oils was almost completely absent in the same subjects after 6 weeks of n-3 fatty acid supplementation. Analysis of fasting concentrations of metabolites and hormones was carried out on the combined data from the two studies. There were no significant differences in total, low-density-lipoprotein- or high-density-lipoprotein-cholesterol concentrations during fish-oil supplementation, although there was considerable individual variation in cholesterol responses to the supplement. Concentrations of Apo-B and Apo-A1 were unchanged during supplementation with fish oils. Fasting and early morning postprandial GIP concentrations were lower in subjects taking fish oils, possibly due to acute effects of fish-oil capsules taken on the evening before the studies. In both studies fasting insulin and glucose and postprandial insulin concentrations remained unchanged following fish-oil supplementation. The results do not support the view that triacylglycerol-lowering effects of n-3 fatty acids are due to modulation of insulin secretion mediated via the enteroinsular axis. Further studies are required to determine the precise mechanism by which fish oils reduce both fasting and postprandial triacylglycerol concentrations.

A longitudinal study of adipose tissue glucose utilization during pregnancy and the puerperium in normal subjects

A longitudinal study of carbohydrate and lipid metabolism in normal pregnant volunteers demonstrated distinct alterations in maternal fuel utilization as pregnancy progresses. Glucose uptake into maternal adipose tissue and plasma glucose levels were significantly reduced in late pregnancy compared to early pregnancy and post-partum values. Plasma fatty acids, glycerol and ketone levels were elevated in late pregnancy. This confirms the concept of the third trimester as a catabolic phase within the maternal system, and provides support for the view that the insulin resistance of pregnancy may be a compensatory response to overcome the inhibitive effects of metabolites such as fatty acids on peripheral uptake of glucose.

Changes in fat, fat-free mass and body water in human normal pregnancy

Measurements of body weight, total body water and total body potassium (40K) were made serially on three occasions during pregnancy and once post partum in 27 normal pregnant women. Skinfold thickness and fat cell diameter were also measured. A model of body composition was formulated to permit the estimation of changes in fat, lean tissue and water content of the maternal body. Total maternal body fat increased during pregnancy, reaching a peak towards the end of the second trimester before diminishing. Serial measurements of fat cell diameter showed poor correlation, whilst total body fat calculated from skinfold thickness correlated well with our estimated values for total body fat in pregnancy.