Chapter 1: Theory of the Analytical Procedure
Chapter 2: Kit Description
Chapter 3: Preparation of Reagent Solutions/Suspensions
Chapter 4: Samples Containing 0 – 12% Fructan
Chapter 5: Samples Containing 12 – 100% Fructan
Chapter 6: Analysis of Fructan Content
Chapter 6A: Hydrolysis of Sucrose & Low DP Maltosaccharides
Chapter 6B: Hydrolysis of Fructan
Chapter 6C: Measurement of Fructan
Chapter 7: Calculation of Fructan Content
50 assays per kit
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|Content:||50 assays per kit|
Short term stability: 2-8oC,
Long term stability: See individual component labels
|Stability:||> 2 years under recommended storage conditions|
|Linear Range:||4 to 80 µg of D-glucose, D-fructose or sucrose per assay|
|Limit of Detection:||1 g/100 g|
|Total Assay Time:||~ 30 min|
|Application examples:||Flours, plant materials (e.g. onion), food products and other materials|
|Method recognition:||This method is a modification of AACC Method 32-32.01 and AOAC Method 999.03|
The Fructan HK test kit is suitable for the specific measurement and analysis of all fructo-oligosaccharides (reducing and non-reducing) and of fructan polysaccharides but is not suitable for the analysis of samples containing high levels of D-glucose, D-fructose, sucrose or maltose. Note that this is a modified version of AOAC method 999.03/AACC Method 32.32.01 (K-FRUC) in which the overall assay principle remains unchanged but detection is performed through the enzymatic hexokinase/glucose-6-phosphate dehydrogenase system as opposed to the reducing sugar PAHBAH determination. The K-FRUCHK procedure has not received official method status.
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- Standard included
McCleary, B. V., Charnock, S. J., Rossiter, P. C., O’Shea, M. F., Power, A. M. & Lloyd, R. M. (2006). Journal of the Science of Food and Agriculture, 86(11), 1648-1661.
Procedures for the measurement of starch, starch damage (gelatinised starch), resistant starch and the amylose/amylopectin content of starch, β-glucan, fructan, glucomannan and galactosyl-sucrose oligosaccharides (raffinose, stachyose and verbascose) in plant material, animal feeds and foods are described. Most of these methods have been successfully subjected to interlaboratory evaluation. All methods are based on the use of enzymes either purified by conventional chromatography or produced using molecular biology techniques. Such methods allow specific, accurate and reliable quantification of a particular component. Problems in calculating the actual weight of galactosyl-sucrose oligosaccharides in test samples are discussed in detail.Hide Abstract
McCleary, B. V., Murphy, A. & Mugford, D. C. (2000). Journal of AOAC International, 83(2), 356-364.
An AOAC collaborative study was conducted to evaluate the accuracy and reliability of an enzyme assay kit procedure for measuring oligofructans and fructan polysaccharide (inulins) in mixed materials and food products. The sample is extracted with hot water, and an aliquot is treated with a mixture of sucrase (a specific sucrose-degrading enzyme), α-amylase, pullulanase, and maltase to hydrolyze sucrose to glucose and fructose, and starch to glucose. These reducing sugars are then reduced to sugar alcohols by treatment with alkaline borohydride solution. The solution is neutralized, and excess borohydride is removed with dilute acetic acid. The fructan is hydrolyzed to fructose and glucose using a mixture of purified exo- and endo-inulinanases (fructanase mixture). The reducing sugars produced (fructose and glucose) are measured with a spectrophotometer after reaction with para-hydroxybenzoic acid hydrazide. The samples analyzed included pure fructan, chocolate, low-fat spread, milk powder, vitamin tablets, onion powder, Jerusalem artichoke flour, wheat stalks, and a sucrose/cellulose control flour. Repeatability relative standard deviations ranged from 2.3 to 7.3%; reproducibility relative standard deviations ranged from 5.0 to 10.8%.Hide Abstract
Measurement of inulin and oligofructan.
McCleary, B. V. & Blakeney, A. B. (1999). Cereal Foods World, 44, 398-406.
Fructans are defined as any compound in which one or more fructosyl-fructose linkages constitute a majority of the linkages (1). This refers to polymeric material as well as to oligomers as small as disaccharide inulobiose. Fructans are widely distributed in the plant kingdom. They are present in monocotyledons, dicotyledons, and green algae. Fructans differ in molecular structure and in molecular weight. They may be classified into three main types, the inulin type, the levan (previously called phlein) type, and the graminan type (2). The inulin group consists of material that has mostly of exclusively the (2-1) fructosly-fructose linkage. Levan is material that contains mostly or exclusively the (2-6) fructosyl-fructose linkage. The graminan (or branched) type has both (2-1) and (2-6) fructosly-fructose linkages in significant amounts (e.g. graminan from Gramineae). The distribution of fructans in nature, and the production of fructooligosaccharides, such as neosugar, using fructosyltransferase, has been reviewed in a monograph (3). In the context of this article and the analytical procedure described, the term fructan relates only to inulin and graminan. The current analytical procedure has not been evaluated on levan.Hide Abstract
Measurement of inulin and inulin-degrading enzymes.
McCleary, B. V. (1998). “Proceedings of the Seventh Seminar on Inulin”, (A. Fuchs and A. Van Laere, Eds.), European Fructan Association, pp. 36-45.
A non-instrumental method for the measurement of fructan is described. The method simplifies fructan analysis, is easy to perform, uses standard laboratory equipment, and is accurate, reproducible and specific. The procedure employs highly purified and specific enzymes to hydrolyse sucrose, starch and fructans (inulins and graminan).Hide Abstract
Fructans - Analytical approaches to a fibre that ferments.
Blakeney, A. B., McCleary, B. V. & Mugford, D. C. (1997). Chemistry in Australia, 17-19.
Fructans are defined as any compound where one or more fructosyl-fructose linkages constitute a majority of the linkages. This refers to polymeric material as well as oligomers as small as the diasaccharide inulobiose. Material included in this definition may or may not contain attached glucose. The terms oligomer and polymer are used by fructan researchers to distinguish between materials that can be specifically characterised and those that can not. Fructans are widely distributed in the plant kingdom. They are present in monocotyledons, dicotyledons and in green algae.Hide Abstract
McCleary, B. V., Gibson, T. S. & Mugford, D. C. (1997). Journal of AOAC International, 80, 571-579.
An American Association of Cereal Chemists/AOAC collaborative study was conducted to evaluate the accuracy and reliability of an enzyme assay kit procedure for measurement of total starch in a range of cereal grains and products. The flour sample is incubated at 95 degrees C with thermostable alpha-amylase to catalyze the hydrolysis of starch to maltodextrins, the pH of the slurry is adjusted, and the slurry is treated with a highly purified amyloglucosidase to quantitatively hydrolyze the dextrins to glucose. Glucose is measured with glucose oxidase-peroxidase reagent. Thirty-two collaborators were sent 16 homogeneous test samples as 8 blind duplicates. These samples included chicken feed pellets, white bread, green peas, high-amylose maize starch, white wheat flour, wheat starch, oat bran, and spaghetti. All samples were analyzed by the standard procedure as detailed above; 4 samples (high-amylose maize starch and wheat starch) were also analyzed by a method that requires the samples to be cooked first in dimethyl sulfoxide (DMSO). Relative standard deviations for repeatability (RSD(r)) ranged from 2.1 to 3.9%, and relative standard deviations for reproducibility (RSD(R)) ranged from 2.9 to 5.7%. The RSD(R) value for high amylose maize starch analyzed by the standard (non-DMSO) procedure was 5.7%; the value was reduced to 2.9% when the DMSO procedure was used, and the determined starch values increased from 86.9 to 97.2%.Hide Abstract
McCleary, B. V. (1994). “Methods in Carbohydrate Chemistry”, Vol. X, (J. N. BeMiller, D. J. Manners and R. J. Sturgeon, Eds.), John Wiley & Sons Inc., pp. 175-182.
A number of methods have been described for the analysis of the fine structure of galactomannans, i.e., the distribution of D-galactosyl units along the D-mannan backbone (1). Such studies include the analysis of x-ray diffraction data of stretched fibers of galactomannans (2,3), 1H- and 13C-nmr (nuclear magnetic resonance) of native and partially depolymerized galacto¬mannans (4) and a range of chemical procedures (5-7), including those employing a detailed theoretical analysis of the kinetics of reaction (8). An alternative approach involves the characterization and quantification of the oligosaccharides produced on hydrolysis of galactomannans by highly purified and well-characterized β-mannanases (EC 18.104.22.168) (9,10). The β-mannanases employed were purified to homogeneity by affinity chromatography on gIucornannan-AH-Sepharose 4B. They were characterized by a range of physicochemicai procedures by determining the kinetics of their action on β-mannooligosaccharides, and by characterizing the structures of oligosaccharides produced on hydrolysis of galactomannans and glucomannans (11). From these studies, a basic model describing the subsite binding requirements of all the β-mannanases examined was proposed (Fig. 1). This model was then modified to account for the slight differences noted in the types of oligosaccharides produced by β-mannanases from different sources. The β-mannanases which differ most significantly in their action patterns on galactomannans are those from Aspergillus niger culture filtrates and from germinated guar seed.Hide Abstract
Yaguchi, S., Shimoda, M., Fukushima, H. & Maeda, T. (2017). Journal of National Fisheries University, 65(1), 1-8.
We investigated the biochemical characteristics of several types of vegetable and fruit powders and the gel strength of Kamaboko mixed with those powders to improve surimi gel quality. Burdock, onion, and carrot powders had high concentrations of fructan and total sugar. Three powders (purple sweet potato, Chinese yam, and East Indian lotus root) contained high amounts of starch. Pectin and polyphenol contents were high in Yuzu powder. Gel strength decreased after mixing with any of the powders. Although polyphenol contents seemed to decrease in the gel strength slightly, it was difficult to estimate gel strength by adding a particular powder and amount.Hide Abstract
de Souza, R. C., Júnior, O. V., Pinheiro, K. H., Klososki, S. J., Pimentel, T. C., Cardozo Filho, L. & Barão, C. E. (2017). LWT-Food Science and Technology, 85, 212-217.
The objective of this study was to evaluate the effect of the addition of β-cyclodextrin, catechin or inclusion complexes (catechin: β-CD) (physical mixture or with supercritical carbon dioxide) on prebiotic green tea beverage characteristics during storage at ambient temperature (90 days/25°C). The prebiotic (oligofructose) stability was also evaluated. The addition of cyclodextrin and/orcatechin resulted in products with higher acidity. The physical process of complexation, which is simple and cheap, gave the best results in relation to the stability of the phenolic compounds content in the product. The supercritical carbon dioxide did not improve the protection of the phenolic compounds. A portion of 200 mL of the green tea had sufficient oligofructose content to be considered a prebiotic product during 90 days of storage. It was possible to formulate green tea beverages with high total phenolic compounds (2525–3307 mg CE/L) and oligofructose content (3.1 g/200 mL) sufficient to consider them prebiotic products, being recommended the physical process of complexation (catechin: β-CD). The green teas would maintain the beneficial effects for 90 days at ambient temperature (25°C).Hide Abstract
R. S. & Singh, R. P. Singh. (2017). “Current Developments in Biotechnology and Bioengineering”, pp 423-446.
Microbial inulinases are an important class of industrial enzymes that have the ability to hydrolyze inulin into either fructose or fructooligosaccharides. Both of the products have commercial applications in many food and pharmaceutical industries. Inulinases have been reported from plants, animals, and microorganisms. They are present in much less quantity in plants and animals, which restricts their exploitation for industrial applications. Because of this limitation, microorganisms are considered as major sources of inulinases. A good number of microbial sources are reported for inulinases and a majority of them belong to fungi and yeasts. On the basis of the action pattern of inulinases on inulin, they are categorized into exoinulinases and endoinulinases. Exoinulinases hydrolyze the terminal linkages present in inulin and produce fructose, whereas endoinulinases act randomly on internal β-2,1 glycosidic linkages of inulin and produce fructooligosaccharides. Apart from the production of fructose and fructooligosaccharides, inulinases have also been used for the production of many other valuable products like bioethanol, single-cell oils, single-cell proteins, citric acid, etc. This chapter is a brief compilation of the production, purification, and applications of the inulinases.Hide Abstract
Pimentel, T. C., Madrona, G. S., Garcia, S. & Prudencio, S. H. (2015). LWT-Food Science and Technology, 63(1), 415-422.
This study aimed to evaluate the effect of the supplementation of clarified apple juice with probiotic Lactobacillus paracasei ssp. paracasei and/or oligofructose (prebiotic and sugar substitute) on the physicochemical characteristics, probiotic viability and on the acceptability during refrigerated storage (4°C for 28 days) in plastic or glass packages. Probiotic juices showed chemical composition, density, acceptability and purchase intent similar to products without supplementation but higher acidity, turbidity and red color. Supplementation with oligofructose did not change the physicochemical characteristics, acceptability, purchase intent and storage stability of the products, and enhanced the probiotic survival during storage. Oligofructose was stable to storage in apple juice and could be used as a sugar substitute as oligofructose added products had similar physicochemical characteristics and acceptability of the products with sucrose. The glass package was more appropriate than the plastic package in maintaining the viability of the probiotic culture, with no effect of packaging (glass or plastic) on the physicochemical characteristics and acceptability of juices.Hide Abstract
Krivorotova, T. & Sereikaite, J. (2014). Acta Physiologiae Plantarum, 36(1), 79-83.
The data on the composition of carbohydrates in Jerusalem artichoke tubers harvested at the end of March after being exposed to frost during winter in soil were presented. The analysis of carbohydrates was also performed during the following period of vegetative growth and intensive photosynthetic activity in summer. Moreover, the composition of carbohydrates in spring tubers was compared with the one in autumn tubers. The tubers of three cultivars Sauliai, Albik and Rubik were applied for the analysis. The amount of fructooligosaccharides in the spring tubers of all cultivars was equal approximately to 80% of dry matter. The similar amount of fructooligosaccharides was determined in the autumn tubers of both Sauliai and Albik. In Rubik tubers, their amount was about 10% higher. The average degree of fructooligosaccharides polymerization differed. In the spring tubers of all cultivars, it was equal to three. In the autumn tubers of Sauliai, Albik and Rubik it was equal to 6, 9 and 10, respectively. The highest amount of sucrose equal to 14–18% depending on the cultivar was found in the spring tubers. The autumn tubers had the low amount of sucrose (1.4–4.3%), glucose (0.07–0.18%) and fructose (0.35–0.5%). The data on the composition of carbohydrates showed that the tubers of Jerusalem artichoke can be harvested in autumn or left in soil for overwintering. However, they should be used for different purposes due to different carbohydrates composition.Hide Abstract
Capriles, V. D. & Arêas, J. A. G. (2013). Food & Function, 4(1), 104-110.
The effect of adding increasing levels of prebiotic inulin-type fructans (ITFs) (0, 4, 8, 10 and 12%) on the sensory and nutritional quality of gluten-free bread (GFB) was assessed. ITFs can provide structure and gas retention during baking, thus improving GFB quality by yielding better specific volume, softer crumb, improved crust and crumb browning with enhanced sensory acceptance. During baking, approximately one-third of the ITFs was lost. The addition of 12% ITFs to the basic formulation is required in order to obtain GFB enriched with 8% ITFs (4 g of fructans per 50 g bread serving size), levels that can provide health benefits. 12% ITFs-addition level decreased GFB glycemic index (from 71 to 48) and glycemic load (from 12 to 8). Prebiotic ITFs are a promising improver for GFB that can provide nutritional (11% dietary fiber content, low glycemic response) and functional benefits to patients with celiac disease, since ITFs are prebiotic ingredients that can also increase calcium absorption.Hide Abstract
Palacio, S., Bueno, C. G., Azorín, J., Maestro, M. & Gómez-García, D. (2013). American Journal of Botany, 100(9), 1790-1799.
• Premise of the study: Wild-boar soil disturbance (i.e., rooting) increases the abundance of some species of geophytes (i.e., plants with underground renewal buds) in upland meadows. However, the mechanisms that could lead to such enhanced prevalence remain unexplored. • Methods: We analyzed the effects of wild-boar disturbance on the size, nutrient (N, P, K, C, and total ash), and nonstructural carbohydrate (soluble sugars, starch plus fructans, and total nonstructural carbohydrate) content of the storage organs of five taxa of upland geophytes. Results were explored in relation to the nutrient availability (total N, available P, and K) in the soil. • Key results: Wild-boar rooting increased the size and the nutrient content of the storage organs of geophytes. Such enhanced storage was further promoted by rooting recurrence and intensity. Although we could not detect a direct impact of rooting on soil nutrient concentrations, plants were clearly N limited and such limitation was ameliorated in areas rooted by wild boar. Furthermore, plant-soil interactions for N were different in rooted areas, where plant N-concentrations responded positively to soil N. • Conclusions: Geophytes growing in rooted areas have an increased nutrient value, which may promote the revisit of wild boars to previously rooted areas, with further positive feed-back effects on plant quality. This plant-animal interaction may shape upland geophyte communities.Hide Abstract
Dodevska, M. S., Djordjevic, B. I., Sobajic, S. S., Miletic, I. D., Djordjevic, P. B. & Dimitrijevic-Sreckovic, V. S. (2013). Food Chemistry, 141(3), 1624-1629.
The typical Serbian diet is characterised by high intake of cereal products and also legumes are often used. The content of total fibre as well as certain fibre fractions was determined in cereals, cereal products, and cooked legumes. The content of total fibre in cooked cereals and cereal products ranged from 2.5 to 20.8 g/100 g, and in cooked legumes from 14.0 to 24.5 g/100 g (on dry matter basis). Distribution of analysed fibre fractions and their quantities differed significantly depending on food groups. Fructans and arabinoxylans were the most significant fibre fractions in rye flakes, and β-glucan in oat flakes, cellulose and resistant starch were present in significant amounts in peas and kidney beans. When the size of regular food portions was taken into consideration, the best sources of total dietary fibre were peas and kidney beans (more than 11 g/serving). The same foods were the best sources of cellulose (4.98 and 3.56 g/serving) and resistant starch (3.90 and 2.83 g/serving). High intake of arabinoxylans and fructans could be accomplished with cooked wheat (3.20 g and 1.60 g/serving, respectively). Oat (1.39 g/serving) and barley flakes (1.30 g/serving) can be recommended as the best sources of β-glucan.Hide Abstract
Whelan, K., Abrahmsohn, O., David, G. J. P., Staudacher, H., Irving, P., Lomer, M. C. E. & Ellis, P. R. (2011). International Journal of Food Sciences and Nutrition, 62(5), 498-503.
Fructans are non-digestible carbohydrates with various nutritional properties including effects on microbial metabolism, mineral absorption and satiety. They are present in a range of plant foods, with wheat being an important source. The aim of the present study was to measure the fructan content of a range of wheat, rye and gluten-free breads consumed in the United Kingdom. Fructans were measured in a range of breads using selective enzymic hydrolysis and spectrophotometry based on the AOAC 999.03 method. The breads generally contained low quantities of fructan (0.61–1.94 g/100 g), with rye bread being the richest source (1.94 g/100 g). Surprisingly, gluten-free bread contained similar quantities of fructan (1.00 g/100 g) as other breads. There was wide variation in fructan content between individual brands of granary (0.76–1.09 g/100 g) and gluten-free breads (0.36–1.79 g/100 g). Although they contain only low quantities of fructan, the widespread consumption of bread may make a significant contribution to fructan intakes.Hide Abstract
Biesiekierski, J. R., Rosella, O., Rose, R., Liels, K., Barrett, J. S., Shepherd, S. J., Gibson, R. & Muir, J. G. (2011). Journal of Human Nutrition and Dietetics, 24(2), 154-176.
Background: Wholegrain grains and cereals contain a wide range of potentially protective factors that are relevant to gastrointestinal health. The prebiotics best studied are fructans [fructooligosaccharides (FOS), inulin] and galactooligosaccharides (GOS). These and other short-chain carbohydrates can also be poorly absorbed in the small intestine (named fermentable oligo-, di- and monosaccharides and polyols; FODMAPs) and may have important implications for the health of the gut. Methods: In the present study, FODMAPs, including fructose in excess of glucose, FOS (nystose, kestose), GOS (raffinose, stachyose) and sugar polyols (sorbitol, mannitol), were quantified using high-performance liquid chromatography with an evaporative light scattering detector. Total fructan was quantified using an enzymic hydrolysis method. Results: Fifty-five commonly consumed grains, breakfast cereals, breads, pulses and biscuits were analysed. Total fructan were the most common short-chain carbohydrate present in cereal grain products and ranged (g per portion as eaten) from 1.12 g in couscous to 0 g in rice; 0.6 g in dark rye bread to 0.07 g in spelt bread; 0.96 g in wheat-free muesli to 0.11 g in oats; and 0.81 g in muesli fruit bar to 0.05 g in potato chips. Raffinose and stachyose were most common in pulses. Conclusions: Composition tables including FODMAPs and prebiotics (FOS and GOS) that are naturally present in food will greatly assist research aimed at understanding their physiological role in the gut.Hide Abstract
Halmos, E. P., Muir, J. G., Barrett, J. S., Deng, M., Shepherd, S. J. & Gibson, P. R. (2010). Alimentary Pharmacology & Therapeutics, 32(7), 925-933.
Background: Although it is recognized that diarrhoea commonly complicates enteral nutrition, the causes remain unknown. Aim: To identify factors associated with diarrhoea in patients receiving enteral nutrition with specific attention to formula composition. Methods: Medical histories of in-patients receiving enteral nutrition were identified by ICD-10-AM coding and randomly selected from the year 2003 to 2008. Clinical and demographic data were extracted. Formulas were classified according to osmolality, fibre and FODMAP (fermentable oligo-, di- and mono-saccharides and polyols) content. Results: Formula FODMAP levels ranged from 10.6 to 36.5 g/day. Of 160 patients receiving enteral nutrition, 61% had diarrhoea. Univariate analysis showed diarrhoea was associated with length of stay >21 days (OR 4.2), enteral nutrition duration >11 days (OR 4.0) and antibiotic use (OR 2.1). After adjusting for influencing variables through a logistic regression model, a greater than five-fold reduction in risk of developing diarrhoea was seen in patients initiated on Isosource 1.5 (P= 0.029; estimated OR 0.18). The only characteristic unique to this formula was its FODMAP content, being 47–71% lower than any other formula. Conclusions: Length of stay and enteral nutrition duration independently predicted diarrhoea development, while being initiated on a lower FODMAP formula reduced the likelihood of diarrhoea. As retrospective evaluation does not support a cause–effect relationship, an interventional study investigating FODMAPs in enteral formula is indicated.Hide Abstract
Hempel, S., Jacob, A. & Rohm, H. (2007). European Food Research and Technology, 224(3), 335-341.
An inulin syrup made from Jerusalem artichoke tubers, either in its commercial form or after ultrafiltration, was freeze-dried and used as a prebiotic ingredient in the small-scale manufacture of wafer crackers. The flours used for the preparation of wafer batters were from wheat, rye or spelt wheat, or 1:1 combinations of wheat flour and rye flour or wheat flour and spelt wheat flour. Batter viscosity was strongly influenced by the selection of the flour type, but remained within technologically acceptable limits. The ultrafiltration of the inulin syrup, using a 1 kDa membrane, resulted in a significant reduction of the content of free sugars and minerals which, in turn, had a significant impact on the CIE-Lab color values of the wafer crackers. Using spelt wheat flour instead of wheat flour significantly increased wafer cracker firmness measured by penetration, as did the incorporation of ultrafiltered freeze-dried instead of native freeze-dried Jerusalem artichoke syrup. Sensory analysis revealed a significant influence of product formulation on appearance, flavor and texture of the wafer crackers. It can be concluded from quality scores, which were calculated by using weighting factors assigned to the sensory attributes, that wheat flour may be partially replaced by rye flour or spelt wheat flour without negatively affecting the sensory properties of the wafer crackers.Hide Abstract
Muir, J. G., Shepherd, S. J., Rosella, O., Rose, R., Barrett, J. S. & Gibson, P. R. (2007). Journal of Agricultural and Food Chemistry, 55(16), 6619-6627.
Fructans are not digested in the small intestines of humans. While many health benefits have been attributed to these carbohydrates, they can cause gastrointestinal symptoms in some individuals. We measured the total fructans in 60 vegetables and 43 fruits using the Megazyme fructan assay. Vegetables with the highest quantity of fructans included garlic, artichoke, shallots, leek bulb, and onions (range, 1.2−17.4 g/100 g fw). Fruits with low, but detectable, fructans included longon, white peach, persimmon, and melon (range, 0.21−0.46 g/100 g fw). The fructan assay was modified to provide an estimate of the average chain length (degree of polymerization) for high fructan vegetables. D-Fructose can also be malabsorbed in the small intestine of humans, so the D-fructose content in some foods was measured to supplement the current food tables. Research in this area will be facilitated through the availability of more comprehensive food composition data.Hide Abstract