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Bread properties and crumb structure

M.G. Scanlon*, M.C. Zghal

Department of Food Science, University of Manitoba, Winnipeg, MB, Canada R3T 2N2

Received 22 March 2001; accepted 18 June 2001

Abstract

The relationship between bread-crumb cellular structure and many aspects of quality in a loaf of white bread justifies investiga-tions of how the structure arises during processing of the dough. Following a brief overview of the development of bread cellularstructure in the dough, three parts of the literature pertaining to crumb appearance (visual texture) and bread quality are reviewed,

with emphasis on the mechanical properties (physical texture) of the crumb. The importance of an objective segmentation of thetwo macroscopic phases (crumb cells and cell walls solids) is emphasised in digital image analysis studies of bread-crumb structure.A review of studies where mechanical properties have been measured in fundamental units has sections on the mechanical proper-

ties of the composite structure and on recent analyses of the mechanical properties of the solid phase. Finally, models which havebeen used to relate structure to mechanical properties will be reviewed with emphasis on the work of Gibson and Ashby [Gibson,L.J., & Ashby, M.F., 1988. Cellular solids: structure & properties. Oxford: Pergamon Press; Gibson, L.J., & Ashby, M.F., 1997.

Cellular solids: structure and properties (2nd ed.). Cambridge: University Press]. It is shown that experimental values of Young’smodulus of bread crumb reside within the Hashin-Shtrikman bounds. Compared with the rule of mixtures, these bounds represent agood (52%) improvement in the ability to predict values for bread crumb moduli (crumb firmness). Using information provided bydigital image analysis, Gibson and Ashby’s relationships between structure (relative density) and mechanical properties can be

modified to incorporate dough processing effects such as dough strain hardening and the effect of gas cell coalescence. # 2001Elsevier Science Ltd. All rights reserved.

Keywords: Bread; Crumb; Mechanical properties; Structure; Review; Image analysis; Processing; Density

1. Introduction

There is little doubt about the importance of bread tomany aspects of humanity and civilisation. Control ofthe production (Coulton, 1925) and distribution (Veyne,1990) of bread has been used as a means of exercisingpolitical influence over the populace for at least the last2000 years. Even today, a shortage of bread is synon-ymous with hard times (Anon, 2000), while the promiseof its surfeit is used as a rallying call for a better life(Kropotkin, 1906). Bread also retains significance inhospitality and matters of social propriety (Blake,1825), so much so, that in the Russian language, theword hospitality is a concatenation of the words forbread and salt (Smith, 1977). A further role for bread,as a ‘‘staff of life’’ (Kahn, 1984), is its religious sig-nificance: in specific circumstances, the bread is believed

to be transformed to a divine state (Powers, 1967), aphenomenon, which when measured by any lengthparameter, marks a substantial phase transition. Thequality of the bread has certainly been an issue in all theseaspects (McCance & Widdowson, 1956), and althoughbread quality is difficult to define (Snyder, 1930), theappearance and the physical texture of the bread aretwo long-held desirable attributes (Seneca, 55).

Therefore, the significance of the commodity itself,and the desire for good quality in the bread, does seemto warrant ‘‘thorough attention’’ by the research com-munity (Batchelor, 1993). The fact that there are inexcess of 16 periodicals1 currently devoted to studies ofcereal science and technology attests to the researcheffort applied to studies of factors (in both milling andbaking), which affect bread quality. However, much ofthe research on bread has focused on perhaps as few asone given quality attribute (Hayman, Hoseney, &

0963-9969/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

PI I : S0963-9969(01 )00109-0

Food Research International 34 (2001) 841–864

www.elsevier.com/locate/foodres

1 Based on a count of cereals science and technology journals

received at the Canadian Grain Commission library, Winnipeg.

* Corresponding author. Tel.: +1-204-474-6480; fax: +1-204-474-

7630.

E-mail address: [email protected] (M.G. Scanlon).

Faubion, 1998a), with researchers studying the linkbetween the chosen quality parameter(s) and raw mate-rials and/or processing conditions as expeditiously aspossible. Even when quantitative structural analysistechniques are employed to analyse bread crumb struc-ture (Batchelor, 1993; Coles & Wang, 1997), the focushas been on linking structural classification para-meter(s) to a comprehensive definition of bread crumbquality (Rogers, Day, & Olewnik, 1995).

The purpose of this review is to focus on the literaturecovering the intermediate stages between raw materialsand overall bread quality. It is based on the premise that‘‘there is a causal connection between the structure andthe way the product behaves’’ (Aguilera & Stanley,1999, p. 417). The relationship between crumb structureand crumb appearance may be self-evident, but thissame crumb structure is also a determinant of loafvolume (Zghal, Scanlon, & Sapirstein, 1999), the resi-lience of the loaf [the typical consumer purchasingdecision assessment test (Ponte & Ovadia, 1996)], thetexture during eating (Kamman, 1970; Pyler, 1988;Taranto, 1983) and even the taste (Baker, 1939). There-fore, some knowledge of the structure that definescrumb appearance will permit us to predict many of thequality attributes of bread from knowledge of theingredients and how they are processed into the cellularstructure on which bread quality is established.

The review addresses three parts of the literature per-taining to crumb appearance, bread crumb physicaltexture and bread quality. In Section 3, the research thathas been devoted to studying the cellular structure ofbread crumb by image analysis will be covered, focusingon the two main methods that have been used to extractcrumb grain features from the image of the cellularstructure. In Section 4, the literature covering themechanical properties of bread crumb will be presented,with emphasis on studies that have provided answers tothe properties of bread crumb in a coherent system ofunits. It is not intended to cover all aspects of changes inthe mechanical properties of bread crumb with time(staling/firming) or the effect of processing on breadtexture; these have been covered in numerous reviews(e.g. Parker & Ring, 2001; Ponte & Ovadia, 1996).However, in order to make the structure/texture link inSection 5, specific mechanical properties and theirdetermination will be highlighted, and this requiressome examination of processing and shelf life. In thefinal part, the literature which has related structure tomechanical properties will be reviewed. This will drawheavily on the properties of cellular solids, especially thework of Gibson and Ashby (1988, 1997) and their co-workers, regardless of whether these structure-proper-ties relationships are for engineering materials, bioma-terials or food materials possessing very differentmechanical properties from bread crumb. The purposeis to identify comprehensive (or perhaps universal)

relationships for cellular solids and see if bread crumbcan be integrated within this framework. Because of thefocus of the review on bread crumb, the next section isan attempt to define white bread crumb in terms of itsmechanical properties and its structure from a cellularsolid viewpoint. This section, although not a compre-hensive overview, is necessary because of the perspectiveon quality that other reviewers of texture and appear-ance of bread crumb may have taken.

2. Formation of the bread crumb

2.1. Bread

Bread as a solid is ‘‘soft’’ (Clark, 1991; Scanlon,Sapirstein, & Fahloul, 2000), and, like many otherfoodstuffs (Campbell & Mougeot, 1999), is comprised,at a macroscopic level, of two phases- a fluid (air) and asolid (cell wall material). When viewing a cross-sectionof bread crumb (Fig. 1), it is apparent that the solidphase is entirely connected (Torquato, 2000); thoseportions that are not, are not bread crumb, but merelybread crumbs. In Fig. 1 it can be seen that the air cellsare isolated. However, in three dimensions, at least aportion (and perhaps most) of the cells are connected.This is evident from microscopic (Gan, Ellis, & Scho-field, 1995) and permeation (Baker, 1939) experiments.The volume fraction of the phases (Ahmed & Jones,1990; Mackenzie, 1950) and the nature of their con-nectivity (Torquato, 1998; Warren & Kraynik, 1997)determines the structure, and consequently the mechan-ical properties of the bread. Therefore, since raw mate-rials and processing conditions determine the structureof the bread, it is pertinent to enquire how the twophases arise in the breadmaking process; a much morecomprehensive account is given in the book, Cereals inBreadmaking, by Eliasson and Larsson (1993).

Fig. 1. Digital image of bread crumb from a loaf prepared by the

Chorleywood Bread Process (courtesy of Dr. Martin Whitworth,

CCFRA, Chipping Campden).

842 M.G. Scanlon, M.C. Zghal / Food Research International 34 (2001) 841–864

2.2. Breadmaking

The mix ingredients that are used to create a basicformula dough are flour, water, leavening agent (yeastor chemicals) and sodium chloride (Brown, 1993; Tip-ples, 1975). In order to convert these mix ingredientsinto the structure shown in Fig. 1 a number of proces-sing operations are performed (Tipples, 1975). Theoperations are carried out in such a way that the doughcan possess the appropriate mechanical propertieswhich will permit it to retain gas and thus produce awell-expanded loaf of bread with an even crumb struc-ture (Bloksma & Bushuk, 1988; Gan et al., 1990;Kokelaar & Prins, 1995). Three objectives are sought inthe processing operations (Kent & Evers, 1994):

1. mixing and development of the dough (mixing andfermenting);

2. formation of a foam structure in the dough(moulding, proofing and baking); and

3. stabilization of a porous structure by altering themolecular configuration of the polymeric compo-nents in the cell walls through the application ofheat (baking).

2.2.1. Mixing and development of the doughAttainment of the first of the objectives in Section 2.2

requires mechanical work input to the dough and adegree of chemical modification of some of the poly-mers in the flour. Traditionally this is achieved bykneading the mix (work input) and allowing time (fer-mentation time) for biochemical and chemical mod-ification of the physicochemical properties of thepolymers (Brown, 1993; Tipples, 1975). With the adventof mechanical dough development processes such as theChorleywood Bread Process (CBP), these two tasksoccur simultaneously in the mixer (Cauvain, 1999; Tip-ples, 1975). Regardless of the manner in which mixingand fermentation are performed, three recognisabletasks are apparent (Bloksma, 1990a; Campbell, Rielly,Fryer, & Sadd, 1991; Kent & Evers, 1994).

2.2.1.1. Hydration. Mixing does more than just dispersethe ingredients homogeneously [well, at a resolution ofhalf a millimetre by the end of mixing (Bloksma &Bushuk, 1988)]. The large amount of water that is addedto the flour has to be absorbed by the flour polymers. Ina typical white flour, approximately 71% of flour weightis carbohydrates (of which the vast majority is starch),13% is protein, 1% is lipids and 14% is water, with anumber of components making up the remainder(Bushuk, 1975). On a weight by weight basis, themajority of the water added to make up the dough isabsorbed by hydrophilic groups on the protein mole-cules (Farrand, 1969), although the extent of starchcrystallite shearing that occurs in the milling process will

alter the extent of water uptake by the starch (Evers,Baker, & Stevens, 1984; Scanlon, Dexter, & Biliaderis,1988).

2.2.1.2. Development of the gluten proteins. Althoughsome of the flour proteins are water-soluble (Bloksma &Bushuk, 1988), it is the insoluble proteins that are thefocus of studies aimed at elucidating how mechanicalwork input converts flour and water into a cohesivedough mass (Weegels, Hamer, & Schofield, 1996). Whenthe dough is optimally developed by the mixer, theproteins (which appear to have complexed with flourlipids and some carbohydrate components) form acoherent viscoelastic mass encapsulating the air (seelater), the starch granules and other filler materials [e.g.small bits of bran (Bloksma, 1990b)]. Optimal glutendevelopment by the mixing process is vital to the devel-opment of structure in the crumb. For example, thedensity of the resulting structure is markedly affected byinsufficient disaggregation of the native gluten polymers(Zghal et al., 1999). Although the composition andstructure of the liquid2 phase is expected to change withsubsequent processing operations, it is the coherent vis-coelastic mass leaving the mixer that is the mothermaterial for the cell wall material in the final crumb.

2.2.1.3. Occlusion of air. One ingredient not mentionedearlier, but which (in volumetric terms) is a significantcomponent of the dough is air. This air arises from airentrapped in the bulk volume of the flour mass (Shimiya& Yano, 1987) or from entrainment during the mixingprocess (Campbell et al., 1991; Cauvain, Whitworth, &Alava, 1999; Chamberlain & Collins, 1979). No new gascells are generated in subsequent operations despite theaction of leavening agents (Baker & Mize, 1941).

Fig. 2. Relationship between volume fraction of gas cell nuclei in the

dough (�) and headspace pressure during mixing for three different

mixers (data courtesy of Dr. Grant Campbell, SCGPE, Manchester).

2 Because leavening operations apply stress slowly, the condensed

phase of dough will be referred to as a liquid (Bloksma, 1981).

M.G. Scanlon, M.C. Zghal / Food Research International 34 (2001) 841–864 843

Therefore, the nuclei for the developing gas cells thatmake up the air phase in the bread crumb must be gen-erated in the mixer, with their volume fraction in thedough being a function of mixer type (as high as 20% ofdough volume in some cases, Whitworth & Alava,1999). One question of interest pertaining to the gasphase is whether increases in the volume fraction of gasentrained during mixing (Fig. 2) are biased towardslarger sizes of the same number of nuclei or towardslarger numbers of the same size (Campbell, Rielly,Fryer, & Sadd, 1998). These differences would beexpected to give rise to cellular solids with differentstructures (Benning, 1969a; Chaffanjon & Verhelst,1992), which in turn will affect some mechanical prop-erties (Brezny & Green, 1990; Chaffanjon & Verhelst,1992). This is particularly true where surface activecomponents contribute to gas cell stabilization (Broo-ker, 1996; Graham & Phillips, 1976) so that interfacecomposition is not identical to that of the bulk. Inexperiments where a vacuum has been drawn duringmixing to decrease the amount of air occluded, it wouldappear that fewer numbers of gas nuclei are entrainedrather than smaller sizes (Campbell et al., 1998;Elmehdi, Page, & Scanlon, 2000).

2.2.2. Formation of a foam structure in the doughThe leavening agent generates gas (CO2) within the

liquid phase, which diffuses in solution to the nuclei dueto a concentration gradient (Chamberlain & Collins,1979; Shah, Campbell, McKee, & Rielly, 1998). As aresult, the nuclei expand into gas cells and the density ofthe dough is reduced. This simplistic picture is compli-cated in a real breadmaking process by the non-inde-pendent nature of gas cell growth and by the actions ofthe baker. Factors associated with gas cell growth (orlack of it) will be considered later, but in a real bread-making process, the baker strives to optimise crumbstructure in the final loaf. Therefore, punching, sheetingand moulding operations will be carried out to redis-tribute leavening agents and gas cells so as to improvecrumb appearance (Tipples, 1975). These operations areless influential in mechanical dough development pro-cesses such as the Chorleywood Bread Process (CBP),where fewer of them occur, so that gas cell set-up fromthe mixer must be more carefully controlled (Campbellet al., 1998; Cauvain, 1999; Chamberlain & Collins,1979). Even so, moulding line interfaces and roll-updefects do occur in CBP bread (Whitworth & Alava,1999), but their effect on bread crumb structure will beignored in this review. Regardless of whether the gas cellnuclei entering the final proof emerge from the mixingaction or from the subdivision of gas cells in the sheet-ing and moulding processes, it is the final proof stagethat is responsible for determining the structure of thebread crumb (Shah et al., 1998). However, the gas cellsin the bread are not an image of the nuclei going into

the final proofer scaled according to a lower density; anumber of factors are responsible for redistribution ofgas cells.

Since there is a distribution of gas cell sizes in thedough (Campbell et al., 1991; Carlson & Bohlin 1978;Cauvain et al., 1999; Whitworth & Alava, 1999), therewill be a distribution of gas cell expansion potentialsacross the volume of the dough piece due to Laplacepressure (Benning, 1969c; Ip & Toguri, 1994). There-fore, even in the absence of gas generation by the yeast,large cells will grow because their lower free energy statewill dictate nitrogen diffusion from the smaller cells tothe larger ones (Shimiya & Yano, 1988; van Vliet, 1999),widening the dispersion of cell sizes even further (Ben-ning, 1969c).

Rearrangement of individual components within theliquid phase and at the gas–liquid interface (Brooker,1996; Gan et al., 1995; Graham & Phillips, 1976;MacRitchie, 1976) will affect surface tension around thegas cell, but there is also displacement of the liquidphase as a whole due to the stress imposed on it by theexpanding bubbles (Bloksma, 1981; Schramm & Wass-muth, 1994). The overall result is some drainage of theliquid phase towards the bottom of the dough piece(Bikerman, 1973), although for wheat flour doughs, theviscosity is sufficiently high (Bloksma, 1990b; Kokelaar& Prins, 1995) that dough structure is not unduly affec-ted by foam drainage. One problem in establishing alink between structure and mechanical properties inbread on the basis of extracting ‘‘representative’’ crumbspecimens from a loaf is that during proofing a gradientin crumb structure develops due to gravity influencingcell sizes within the dough. For a dough piece 10 cmhigh, a pressure difference of 1200 Pa will occur betweentop and bottom. Since the driving force for gas cellexpansion is pressure exerted by the CO2 in the cells,and an average excess pressure has been measured at3000 Pa (Bailey, 1955), then a unit mass of CO2 canproduce less expansion in the cells at the bottom. Forpolyurethane foam formation in experiments wheregravitational forces become insignificant, a more homo-geneous distribution of gas cell sizes develops (Noever etal., 1996).

As the gas cells expand beyond a volume fraction ofapproximately 0.74 (Bloksma, 1981; van Vliet, Janssen,Bloksma, & Walstra, 1992), further expansion of the gascell is no longer independent of the expansion of neigh-bouring cells, although independence is likely lost at amuch lower volume fraction as dough flow fields inter-act around adjacent expanding cells (Shah et al., 1998).The polyhedral gas cells that arise because of the stressesexerted on the intervening cell wall material shifts thefocus on foam structure to one of faces, edges and vertices(Gibson & Ashby, 1988) and a balance between surfaceand volume (bulk) forces (Schramm & Wassmuth, 1994;van Vliet et al., 1992). At this stage, coalescence of gas


cells becomes an issue (Prins, 1988; van Vliet et al.,1992). Certain ingredients are known to exert a stabi-lizing influence and retard coalescence (Gan et al.,1995), while non-starchy endosperm components in thedough can initiate holes (Gan, Ellis, Vaughan, & Gal-liard, 1989) that lead to exponential growth of the holewithin the cell wall and redistribution of the liquidphase towards cell vertices (Dalnoki-Veress, Nickel,Roth, & Dutcher, 1999). It has been suggested thatorientation of glutenin polymers leads to a strain hard-ening effect which maintains gas cell integrity(Dobraszczyk & Roberts, 1994; van Vliet et al., 1992).Bulk rheological descriptions of the dough are no longervalid since the walls between some gas cells appear to bethinner than the large starch granules (Gan et al., 1990;Sandstedt, Schaumburg, & Fleming, 1954). To optimisebread quality, a compromise is sought in achieving asfew defects as possible, so that optimal structure ismaintained, while maximizing loaf volume due to con-tinued expansion of the integral gas cells. It has beenintimated that in modern north American breadmakingresearch programmes, the emphasis has been on thelatter (Hayman et al., 1998a).

2.2.3. Stabilization of porous structureAlthough some of the discussion on cell contiguity

and gas cell coalescence may be more relevant to thebaking process than the proofing stage (Burhans &

Clapp, 1942; Hayman, Hoseney, & Faubion, 1998b; He& Hoseney, 1991), it is only in the oven that the finalbread crumb structure is set by conversion of the liquidphase to a solid one. This occurs because, at the tem-peratures and moisture contents typical for bread bak-ing, thermal transitions occur. One class of polymerswithin the gluten proteins are known to undergo aggre-gation (Weegels, de Groot, Verhoek, & Hamer, 1994);rigidity is conferred to the structure when the polymersare more effectively cross-linked (Muller, 1969). Butassociation of gluten polymer chains with numerousother components is also expected (Blanshard, 1986).The other major class of polymers in dough cell walls isalso affected by the heat–moisture regime of the bakingprocess. Partial melting of the hydrated starch granulesis induced (Donovan, 1979), but not their completehomogenization (Keetels, Visser, van Vliet, Jurgens, &Walstra, 1996d), so that individual granules are readilyrecognisable in the bread (Hug-Iten, Handschin, Conde-Petit, & Escher, 1999; Sandstedt et al., 1954). Moleculesexuded from the starch granules also contribute to themyriad of molecular associations (Biliaderis, 1991;Martin, Zeleznak, & Hoseney, 1991), ensuring that thecell wall material is truly a complex composite (Blan-shard, 1986). Once these thermal transitions haveoccurred, further expansion of the gas cells is limited bythe large viscosity of the cell walls, implying that furtherexertion of stress by gas expansion may lead to tensile

Fig. 3. Schematic to illustrate the progression of nucleation, gas cell growth and partial coalescence events in a dough leading to creation of bread

crumb cellular structure.


failure and opening up of the cell wall faces (Bloksma,1990a; Fan, Mitchell, & Blanshard, 1999).

Because the original starch granules covered a dis-tribution of sizes, essentially bimodal (Soulaka & Mor-rison, 1985a), the retention of some recognisable starchgranule morphology infers that the distribution ofstarch granule sizes within the solid phase will exert aneffect on the properties of the crumb cell walls (Luyten& van Vliet, 1995), and hence influence the macroscopicphysical properties of the bread crumb (Soulaka &Morrison, 1985b). Because the mechanical properties ofstarch gels are affected by the degree of melting and theconcentration of starch (Evans & Lips, 1992; Ring,1985), crumb wall mechanical properties would beexpected to vary microscopically and macroscopically;microscopically because the finite thicknesses of the cellwalls will determine the volume fraction of granules inthe walls, and macroscopically because variation incrumb moisture content across the loaf will dictate dif-ferences in the degree of melting of the starch granules(Noel, Ring, & Whittam, 1993; Varriano-Marston, Ke,Huang, & Ponte, 1980). Thus, not only are gradientsexpected within the loaf for the gas phase (Section2.2.2), but also for the solid phase, both of which willaffect crumb mechanical properties. A final confound-ing factor in crumb structure is the finite time necessaryfor heat transfer into the dough mass. As a result, theheat-set cellular structure of the outer regions of the loafwill be compressed by the pressure exerted by the ovenspring phenomenon occurring in the inner region of thedough mass/loaf (He & Hoseney, 1991), so that theouter cells will be elongated with their long axes parallelto the crust planes.

Therefore, the final structure of bread crumb is, at amacroscopic level, a two phase system of randomly dis-persed gas at a high volume fraction (f50.8) in amatrix whose cell walls of thickness, 20–200 mm (Cha-bot, Hood, & Liboff, 1979; Gan et al., 1995) and beyond(Hug-Iten et al., 1999), are more open than closed. At amicroscopic level, the cell walls themselves are nothomogeneous but are comprised of semi-swollen starchgranules interlinked by a complex mixture of aggregatedmolecules, and perhaps comprising a microscopic two-phase system of gas cells within the solid components ofthe cell walls (Zghal et al., 1999).

3. Evaluating bread crumb cellular structure

The terms crumb texture and crumb grain are usedinterchangeably to describe the cellular structure of thecrumb at a cut surface when a loaf of bread is sliced(Kamman, 1970). In general, though, the term textureusually refers to sensory perceptions associated with themechanical properties of foods. Bourne (1982) has indi-cated that, in the case of bread crumb evaluations, the

term texture appears to be used exclusively to describecrumb uniformity and distribution of cell sizes. Theterm texture is also used in image analysis to indicatevariegation in surface profile which leads to variation inintensity within the image (Davies, 2000). Variegationdue to a distribution of surface heights is evidently thecase for the cut surface of bread crumb (Pedreschi,Aguilera, & Brown, 2000). Therefore, to avoid conflictwith the term texture, the term physical texture will beused to refer to the mechanical properties of bread, andvisual texture to describe crumb cellular structure.

Crumb cellular structure (or its grain) is an importantquality criterion used in commercial baking and researchlaboratories to judge bread quality alongside taste,crumb colour and crumb physical texture (Kamman,1970; Pyler, 1988; Zayas, 1993). Bread crumb visualtexture accounts for approximately 20% of the weightingused in judging bread quality (Pyler, 1988). Regardlessof the weight assigned to it, crumb grain is believed tohave considerable importance in defining bread qualitysince the accuracy in scoring other quality attributes inbread (e.g. loaf volume, loaf symmetry) depends on theunderlying crumb grain characteristics.

In bread crumb scoring, the examined parameters arecrumb fineness (open versus closed cells), uniformity,cell shape, and cell wall thickness (Pyler, 1988). Thetraditional method for crumb grain scoring or inspec-tion is qualitative and subjective in nature since it relieson human vision which is known to be inconsistentamong different experts (Wang & Coles, 1994) and canvary over a period of time even for the same expert. Thedevelopment of a modern baking industry, which usesautomated and continuous processes, necessitates moresophisticated methods that are fast, precise, consistentand reliable (Chan & Batchelor, 1993) when evaluatingthe quality of finished bakery products such as breadand other baked goods. In recent years, there has beenincreasing interest in adapting digital image analysis forobjective and quantitative evaluation of bread crumbgrain. A number of investigators have studied the cel-lular structure of bread crumb using different methods(Bertrand, Le Guerneve, Marion, Devaux, & Robert,1992; Rogers et al., 1995; Sapirstein, Roller, & Bushuk,1994; Wang & Coles, 1994; Zayas, 1993).

3.1. Image acquisition

In examining the visual texture of bread, particularlyif one is trying to obtain quantitative information on itsstructural organisation to determine the influence offormula or processing conditions (Lewis, Kijak, Reuter,& Szabat, 1996), the goal is to enhance the contrastbetween the two phases in the image (Hall & Bracchini,1997; Harrel, 1930; Nieh, Kinney, Wadsworth, & Ladd,1998). This is essential if accurate information on thevolume fraction of the two phases is required (Narine &


Marangoni, 1999). In examining the structure of othercellular products, a number of image acquisition meth-ods have been used including:

1. transmission of light through thin sections (Lewiset al., 1996; Schwartz & Bomberg, 1991), wherethe solid phase appears at the low end of the greylevel scale;

2. reflection of light from the surface of the specimen(Hall & Bracchini, 1997), where the shadows castby cut cell walls attenuate the light intensity that isreflected from the recessed cell walls, so that thesolid phase appears at the high end of the greylevel scale; and

3. x-ray tomography (Coker, Torquato, & Duns-muir, 1996; Nieh et al., 1998), where differences inabsorption between the two phases permits non-destructive evaluation of the internal structure.

In some cases of measurements of surface structure,reagents have been added to enhance the contrastbetween the two phases (Harrel, 1930; Shimiya &Nakamura, 1997). It appears that only reflected lighttechniques have been used in image analysis evaluationsof bread crumb structure.

To acquire the digital image of the cut surface of thebread crumb, three elements are necessary—a source ofillumination, the specimen and an image sensing device(Chan & Batchelor, 1993). According to Chan andBatchelor (1993), ‘‘the importance of lighting cannot beover-emphasised’’, particularly for bread crumb, wherecrumb structure makes for a complex visual texture(Batchelor, 1993; Wang & Coles, 1994). Over 70 yearsago, Harrel (1930) demonstrated how the contrast incrumb grain was markedly affected by the angle of illu-mination on the specimen surface, since the distinctionbetween cells and walls at the surface is enhanced (Hall& Bracchini, 1997). Although image quality is a func-tion of a number of parameters (Schade, 1987), enhan-cing the contrast in the image (Fig. 4) is of benefit formaximizing the information that can be gleaned fromthe image (Peli, 1990).

Once acquired, the image is then processed in order toextract information on crumb grain features that can beused to quantify the visual texture of the bread crumb.Thus far, two strategies have been employed to achievethis, and they can be generally classified as techniquesbased on image texture analysis or cell segmentation.

3.2. Image texture analysis

Image texture analysis is a region descriptiveapproach that provides a measure of properties such assmoothness, coarseness and regularity (Gonzalez &Wintz, 1983). It has been used to extract bread crumbcharacteristics, which are then used mainly for scoringpurposes.

The first application of video image analysis todescribe the textural appearance of white bread crumbwas performed by Bertrand et al. in 1992. They char-acterized bread crumb from seven bread formulationsdiffering in surfactant composition using mathematicalmethods based on a two-dimensional Haar transform.This method permitted the extraction of 66 texture char-acteristics per image, each corresponding to a coefficientdetermined according to the size of the Haar mask used.Stepwise discriminant analysis was performed to identifyimages of bread crumb according to the experimentaltreatments. Six texture characteristics permitted 82% ofbread images to be correctly classified according to sur-factant type used in the bread formulation.

Zayas (1993) evaluated the crumb grain of two com-mercial bread brands by digital image texture analysisof a whole slice using a statistical approach. Breadcrumb features were extracted based on first-order sta-tistical measures (e.g. mean and variance) and second-order statistical measures (e.g. contrast). Multivariatediscriminant analysis, which was applied to the imagetexture features to distinguish the two brands of bread,resulted in more than 97% of the images of bread slicesbeing correctly identified. A ranking scale was devel-oped on the basis of percent fineness or coarseness ofsub-images within a bread slice. The author indicatedthat this scale was flexible and could be adapted to meetthe requirements of laboratory and commercial usersfor bread scoring. Although this method was shown tobe effective in evaluating the visual texture of breadcrumb, the long computational time required for featureextraction may limit its practical application (Wang &Coles, 1994).

Fig. 4. Dependence of root mean square (RMS) contrast (Peli, 1990)

in digital images of bread crumb as a function of angle of illumination

(Harrel, 1930). Results imply a compromise between enhancing con-

trast and attaining precision (image data courtesy of Dr. Harry

Sapirstein and Mr. Randy Roller, University of Manitoba).


In another study, Zayas, Steele, Weaver, and Walker(1993) investigated the sensitivity of image texture ana-lysis of crumb grain along with shape and size char-acteristics of the bread slice for differentiation of breadsaccording to ingredient and processing factors. Imagefeatures were extracted from co-occurrence matrices of64�64 pixel sub-images. This approach of featuresextraction considered not only the distribution of greylevel intensities, but also the positions of pixels withequal or nearly equal intensity values. Zayas and cow-orkers (1993) indicated that co-occurrence matrix andgrey level features characterized crumb grain effectivelyand allowed ranking of sub-images according to poros-ity patterns. They also reported that differences in waterabsorption and mixing time were better identified byimage texture features, whereas the presence of short-ening in the bread formulation was distinguished byslice shape features.

Wang and Coles (1994) developed a spatial methodfor image texture analysis based on experience derivedfrom previous studies. Their objective was to enhancethe speed and precision of image analysis for predictingbread scores. In their study, bread images were firstprocessed by edge detection, and then subdivided intosub-images from which crumb features were derivedfrom statistics of grey level values. This method ignoredsub-images containing large bubbles in order to mini-mize their catastrophic effect on bread scoring; this rea-soning was based on the understanding that these largebubbles were overlooked by bread judges during scoring(Coles & Wang, 1997). The average edge density, whichwas calculated from the density of bubble edges in eachsub-image after eliminating 20% of the smallest values,was used as a texture fineness index (Wang & Coles,1994). For two batches of bread samples, the experi-mental results showed that the fineness indices werehighly correlated with subjective scores of expert judges(r250.91). Despite the strength of this relationship, thisapproach may not be effective in evaluating other typesof breads or even the same bread using different scoringstandards, due in part to the subjective elimination oflarge bubbles with no defined cell size threshold. Inaddition, local processing of sub-images may cause anoverestimation of crumb fineness, especially in breadwith a coarse grain. This is because portions of crumbcells lying on the border of a sub-image (sectioned as aresult of local processing) are considered to be small insize, when in fact they are only sections of larger cells.

Day and Rogers (1996) and Rogers et al. (1995) alsoprocessed sub-images of the bread slice, but extractedfeatures from the frequency domain. These featureswere used to characterize crumb fineness and crumb cellelongation. Images were acquired with a documentscanner, so that there may be issues of image qualitybecause of the importance to image analysis of usinglighting that can be adjusted to emphasise structural

features (Batchelor, 1993; Chan & Batchelor, 1993).Despite the absence of configurable lighting, Rogers etal. (1995) showed that their system was capable ofaccurately estimating loaf volume (r2=0.96), computingcrust thickness, and determining crust colour relative tothat of the crumb.

3.3. Cell segmentation

Image segmentation is a process that separates orclassifies object(s) of interest within an image from itsbackground, typically yielding a binary image. Thresh-olding and edge detection are segmentation methodswhich are based on discontinuity of grey-level valueswithin a digital image (Gonzalez & Wintz, 1983). Thegoal in segmenting an image of bread crumb on thebasis of individual cells is to accurately segregate the gasand solid phases, and define the distribution of cell andcell wall sizes. In principle, the analysis could be per-formed in the frequency domain, but the complicatedtexture associated with bread crumb hinders measure-ments of cell sizes (Davies, 2000). Using dominantspectral features of an image tended to overestimate cellsizes in foams with a more regular distribution of gascell sizes than is found in bread crumb (Hall & Brac-chini, 1997).

In analysing the visual texture of extruded flat breads,Smolarz, van Hecke, and Bouvier (1989) used an erosiontechnique to define boundaries of gas cells after subjectivethresholding was performed. The cell segmentationapproach taken by Sapirstein et al. (1994) was to applythe K-means algorithm to automatically and objectivelyascertain a grey level threshold for segmenting eachbread image into the two phases (K=2). In a recentpublication, Sapirstein (1999) stated that the algorithmaccounts for significant variations in the overall reflec-tance of bread crumb images caused by differences incellular structure. The validity of this approach wasdemonstrated in the 1994 publication, by clearly differ-entiating crumb grain of oxidized and non-oxidizedbread. Coles and Wang (1997) also used crumb cellsegmentation to distinguish the two phases and measurethe distribution of crumb cell sizes, which was thencorrelated to the bread’s crumb score. The advantage ofutilizing spatial segmentation for feature extraction isthat, in addition to it being able to provide an estima-tion of crumb fineness, it can also accurately measurevarious structural parameters of the bread crumb. Thecomputed crumb grain features determined bySapirstein et al. (1994) included cell size, cell size dis-tribution, number of cells per unit area, cell wallthickness distribution and void fraction. The impor-tance of properly delineating the two phases is evidentfrom Fig. 5, where measurement of areal density ofcrumb cells is strongly influenced by the grey level cho-sen for segmentation.


Although the segmentation algorithm of Sapirstein etal. (1994) produced a satisfactory classification of ima-ges into crumb cells and cell walls, they pointed out thatthis algorithm tended to underestimate the void fractionand overestimate cell wall thickness, a deficiency con-firmed by Zghal et al. (1999) on the basis of densitymeasurements. Although extrapolating surface tovolume measurement is not always straightforward(Moreau, Velde & Terribile, 1999), difficulties in con-sistent segmentation of the surface image are oftenattributable to the complex cellular structure of breadcrumb. The non-uniform structure of bread crumbcomprises a wide distribution of cell sizes with regionshaving large numbers of small cells while others haveonly a few large cells. Because the intensity of thereflected light (or crumb brightness) depends on thecellular structure of the bread crumb, regions with finerstructure reflect more light, whereas regions with coar-ser structure reflect less light (Burhans & Clapp, 1942;van Vliet et al., 1992). Therefore, selecting a singlethreshold value for segmentation would lead to under-and over-estimation of the cell sizes in finer and coarsercrumb areas, respectively. In order to overcome thislimitation and deal with the complex and subtle detailsof a bread crumb image, a more sophisticated segmen-tation approach such as a multiple thresholding techni-que is required; an example is local segmentation wherea neighbourhood of pixels is used to detect individualobjects within an image (Eggleston, 1998), or individualcrumb cells in the case of bread crumb. This approachdetermines a grey level threshold for each crumb cell,and therefore it accounts for the variation in the cellularstructure within the bread slice.

4. Mechanical properties of bread crumb

4.1. Defining bread behaviour

The evaluation of the mechanical properties of breadcrumb is important not only for routine quality assur-ance in the baking industry, but also for assessing theeffects of changes in various dough ingredients andprocessing conditions, and also the effect of shelf life onacceptability of bread to the consumer (Baruch &Atkins, 1989). As stated earlier (Section 2.1), bread is acomposite solid, comprised, at a macroscopic level, ofcrumb cells full of air in a matrix that is solid, albeit aviscoelastic solid (Hallberg & Chinachoti, 1992).

The mechanical behaviour of the cellular bread crumbitself is known to be complex. This behaviour has beendescribed as non-linear viscoelastic (Hibberd & Parker,1985), and the range of stresses over which bread crumbbehaves in an elastic (Lasztity, 1980) or linear viscoe-lastic manner (Persaud, Faubion, & Ponte, 1990) isnarrow and perhaps poorly defined (Peleg, 1997). Simi-larly, a narrow range of strain (a few percent) has beenreported for the size of the elastic regime of syntheticcellular solids (Gibson & Ashby, 1997). Difficulty incharacterizing the stress strain curve of bread crumbwas attributed in part to its porous structure, in which acomplex combination of stresses arise when a breadspecimen is subjected to mechanical testing (Lasztity,1980; Ponte & Faubion, 1987). In addition, lack ofhomogeneity in the distribution of cells within the breadcrumb also contributes to its complex mechanical beha-viour. This heterogeneity is known to potentially causegreater differences in the mechanical properties of breadcrumb within a single loaf than between loaves of dif-ferent treatments (Ponte & Faubion, 1987). Ponte, Tit-comb, and Cotton (1962) and Short and Roberts (1971)showed that bread crumb firmness, determined bycompression testing, varied across bread slices with thehighest value in the centre. This finding was later con-firmed by Hibberd and Parker (1985) who studied fac-tors causing variability in bread firming measurements.They demonstrated that bread crumb was not homo-geneous in terms of its physical texture, which is notunexpected given the mechanisms of crumb formationdescribed earlier. Nevertheless, a precise quantificationof the mechanical behaviour of bread crumb is desirablebecause the elastic properties of bread crumb have beenconsidered as key factors of bread quality (Nussino-vitch, Steffens, & Chinachoti, 1992a; Piazza & Masi,1995; Wassermann, 1973).

4.2. Measuring crumb mechanical properties

4.2.1. CompressionThe most commonly used method to measure crumb

physical texture is indentation (AACC, 1983; Ponte &

Fig. 5. Change in crumb cell density (number of cells per cm2) as a

function of the grey level threshold used to segment the image into

crumb cells and solid phase for control bread crumb (&), control

bread crumb which had been air-dried for 30 min (~), and bread

prepared from dough that had been sub-optimally mixed ( ). Imaging

data from Zghal et al. (1999). Data are normalized relative to crumb

cell density at the grey level selected by the K-means algorithm as the

optimal threshold, so that all three curves pass through {1, 1}.


Ovadia, 1996), a compressive loading test from which‘‘modulus’’ values can be obtained (Cornford, Axford,& Elton, 1964). Deformation of a crumb specimenbetween parallel plates in a uniaxial compression testcan also be used to measure the mechanical propertiesof bread crumb (Chuah & Scanlon, 2001; Piazza &Masi, 1995). These instrumental measurements of breadfirmness, which are analogous to the subjective methodof assessing crumb firmness by touch or mouthfeel, havebeen shown to correlate well to sensory measurements(Axford, Colwell, Cornford, & Elton, 1968; Bashford &Hartung 1976; Brady & Mayer, 1985). Numerousadvantages are claimed for the compression test (Luy-ten, van Vliet, & Walstra, 1992) including simplicity,since performing the test requires only a small samplesize that can be easily prepared; and validity, sincemechanical properties are measured in a coherent sys-tem of units for which standardized testing protocolshave been rigorously evaluated (Charalambides, Wil-liams, & Chakrabarti, 1995). Fig. 6 shows a typicalstress–strain curve for bread crumb under compression,to indicate two important parameters used for char-acterizing the properties of the bread crumb: Young’smodulus and critical stress.

Compressive testing of bread crumb cubes showedthat the mechanical properties of bread crumb are ani-sotropic (Hibberd & Parker, 1985). Bread crumb stres-sed parallel to the loaf’s longest axis had values forYoung’s modulus 2–3 times those of specimens com-pressed in the other two directions, and values for cri-tical stress 2–2.5 times those in the other directions.Based on the information given in their Fig. 2 for freshbread specimens compressed parallel to the long axis ofthe loaf, values for Young’s modulus ranged from 8 to18 kN m�2; values for the critical stress ranged from 760to 1350 N m�2. Uniaxial compression of wheat starchbread (also tested fresh) gave a value of 18 kN m�2 for

the compressive modulus of crumb specimens com-pressed parallel to the long axis (Keetels et al., 1996d).Fresh specimens of a soft wheat flour bread, compressedparallel to the long axis of the loaf, yielded rather lowvalues for the compressive modulus at 300 N m�2

(Piazza & Masi, 1995).

4.2.2. TensionTensile tests have rarely been used for testing the tex-

ture of bread or other spongy foods. Two reasons wereattributed for their limited use. Firstly, there is difficultygripping the specimen, to ensure lack of compliance atthe grips (Chen, Whitney, & Peleg, 1994; Luyten et al.,1992), or the stress concentration that is created at thegrips can initiate fractures remote from the guage of thespecimen. Secondly, ensuring a valid test requiresadherence to specimen size, shape and stiffness stipula-tions that are difficult to obtain for many foodstuffs(Goh, Charalambides, & Williams, 2000). Despite theselimitations, the tensile test has a number of advantagesover the compression test, in that it provides parameterswhich are simple to interpret (Nussinovitch, Roy, &Peleg, 1990) and better reflect the fundamentalmechanical properties of materials in general. In thecase of bread, tensile loading can be a means of evalu-ating the work required to fracture the crumb, whichcan be used to define crumb coherence and its resistanceto tearing (Scanlon, Fahloul, & Sapirstein, 1997). Fur-thermore, when specimens are subjected to tensile test-ing, the fracture starts at the outside of the specimen,and thus the mechanical behaviour can be clearlyobserved and understood, whereas, in the compressiontest the fracture starts from the inside (Luyten et al.,1992). The sensitivity of tensile tests for detectingdefects in specimens allows the observer to examine theeffect of artificially made notches on fracture behaviour,and therefore, evaluate the notch-sensitivity (Scanlon etal., 2000) and the inherent defect size of the materialstested (Luyten et al., 1992).

Fig. 6 shows a curve for tensile testing of breadcrumb. Because buckling is absent in tension (Peleg,1997), it is evident that a critical stress for the cell wallscannot be assigned. A failure stress (�f) is easily identi-fied, as is an initially linear region from which Young’smodulus can be derived. Close similarity has beenobserved for the average value for the compressive cri-tical stress (1050 N m�2) of Hibberd and Parker (1985)and the average tensile failure stress (1100 N m�2)reported by Scanlon et al. (2000). (For no real apparentreason given differences in specimen preparation andexperimental conditions, other than both studies loadedspecimens parallel to the loaf’s long axis.)

Values for Young’s modulus under tensile loadinghave been reported as 10.6 and 12.5 kN m�2 for 1-dayold bread crumb prepared from strong and extra strongflour and prepared according to commercial practice

Fig. 6. Typical stress strain curves for bread crumb under tensile and

compressive loading. Young’s modulus (E), critical stress (�c), and

failure stress (�f) denoted.


(Scanlon et al., 2000). For bread prepared underlaboratory baking conditions from the same wheats, butloaded in tension parallel to the vertical axis of the loaf,values for Young’s modulus were 8.0 and 7.0 kN m�2,respectively (Zghal, Scanlon, & Sapirstein, 2001a). Bothstudies imply that tensile moduli are of similar magni-tude to the compressive moduli obtained by Hibberdand Parker (1985). Considerably larger values have beenobtained when very small strain (0.02%) dynamic com-pressive/tensile tests have been used to determine themechanical properties of bread crumb: a value ofapproximately 50 kN m�2 having been obtained for theelastic part of Young’s modulus (Davidou, Le Meste,Debever, & Bekaert, 1996).

The ability to propagate a crack in bread crumb spe-cimens with a long notch means that it is possible toderive a fracture toughness value for bread crumb.Using a technique that incorporates all the non-elasticwork within the toughness value (Andrews, 1974),Scanlon et al. (1997) obtained toughness values between4.1 and 7.4 J m�2 for bread crumb, with the greatervalue for the specimen made from extra strong wheat.Given the large hysteresis values for bread crumb(Nussinovitch, Steffens, Chinachoti, & Peleg, 1992b;Scanlon et al., 2000), these values for toughness willlikely be much larger than values obtained by otherfracture techniques (Luyten & van Vliet, 1995).

4.2.3. ShearSmall strain rheometric testing of bread crumb has

been performed (Persaud et al., 1990). A value of 10 kNm�2 was reported for the complex shear modulus (jG*j)of 1 day old bread. No differences in shear moduluswere observed for specimens taken and tested fromvarious orientations within the loaf. Notwithstanding

the assumption of whether bread crumb specimens canbe considered isotropic and homogeneous, the valuesfor Young’s modulus and shear modulus from thesestudies imply that the Poisson’s ratio of bread crumb isfairly low. Low strain experimental measurements of thePoisson’s ratio of white bread crumb confirm this, atvalues of 0.2 (Charalambides, 1997) or 0.21 (Rohm,Jaros, & deHaan, 1997).

A non-comprehensive summary of reported values forthe mechanical properties of bread crumb is given inTable 1.

4.3. Measuring mechanical properties of cell walls

Although the mechanical properties of the bread are afunction of the crumb cell wall materials and the struc-ture created by processing, changes in bread crumbphysical texture with shelf life (staling) are ascribedsolely to cell wall property changes (Guy & Wren,1968). A number of factors account for this. Of the twophases in bread crumb, only the physical properties ofthe solid phase will change (Fearn & Russell, 1982).Most studies indicate that changes in the starch poly-mers in the crumb walls are responsible for the firmingof bread crumb over time (Blanshard, 1986; Parker &Ring, 2001; Zobel & Kulp, 1996), although loss ofmoisture will evidently contribute to a change in theproperties of the cell walls (Hutchinson, Mantle, &Smith, 1989) which would be manifest as a firming ofthe crumb (Piazza & Masi, 1995). Changes in breadcrumb structure are not usually discussed in relation tostaling (Zobel & Kulp, 1996), even though image ana-lysis studies (Zghal et al., 1999) indicated substantialstructural changes arising from crumb moisture losses,with the magnitude of these changes dependent on flour

Table 1

Range of mechanical properties reported for white bread crumb (1-day old or less)

Mechanical parameter Values Mechanical parameter Values

Young’s modulus Critical stresses

parallel to long axisa 8-18 kN m�2 parallel to long axis

parallel to loaf heighta 3-6.5 kN m�2 (compression)a 760–1350 N m�2

dynamic storage modulusb 50 kN m�2 failure (tension)d 710–2280 N m�2

parallel to loaf height

(compression)a 690–900 N m�2

failure (tension)e 910–3160 N m�2

Shear modulus Poisson’s ratio

dynamic storage modulusc 10 kN m�2 small strainf 0.17–0.25

large strainf 0.07–0.15

Fracture toughnessg «7 J m�2

a Hibberd and Parker (1985).b Davidou et al. (1996).c Persaud et al. (1990).d Scanlon et al. (2000), both wheat flours.e Zghal et al. (2001a), all wheats, both water absorptions, optimally proofed.f Rohm et al. (1997).g Scanlon et al. (1997).


type used to make the crumb. Therefore, to eliminatestructural rearrangements within the crumb fromaffecting studies of firming mechanisms within crumbwall components, direct measurement of the propertiesof the solid phase is desirable (Fearn & Russell, 1982;Guy & Wren, 1968).

The most common method of measuring themechanical properties of the solid phase is to performmechanical measurements on the compressed crumb(Guy & Wren, 1968; Hallberg & Chinachoti, 1992;LeMeste, Huang, Panama, Anderson, & Lentz, 1992;Scanlon et al., 2000). Substantial pressures have beenused, sometimes after the crumb has been ground up(LeMeste et al., 1992), to be assured that the macro-scopic two-phase structure of the crumb cannot influ-ence the result. From experimental details provided,rough estimates of the degree of densification rangefrom 5 (Scanlon et al., 2000), through 7 (Baik & Chi-nachoti, 2000) to an unrealistic 20–40 (LeMeste et al.,1992). Alternatively, mechanical measurements are per-formed on (Rolee & Le Meste, 1997; Vodovotz & Chi-nachoti, 1996), or extrapolated to (Keetels, van Vliet, &Walstra, 1996a), starch gels of similar water content tothat of bread crumb, on the grounds that starch is thedominant material in the solid phase (Keetels et al.,1996d). A potential artefact of the compression techni-que is that it may not just eliminate the macroscopicstructure of the bread crumb. It is conceivable that thestructural organisation of components within the solidphase (Hug-Iten et al., 1999; Keetels, van Vliet, & Wal-stra, 1996b) may be critical to the manner by whichfirming develops in the bread crumb. Therefore, ineliminating the effect of the macroscopic structure bydensification, the concomitant changes in microscopicstructure may alter cell wall mechanical properties.

A number of techniques have been employed fordetermining the mechanical properties of these cell wallmaterials, utilizing large and small strain analyses.Large strain tensile evaluations of compressed breadcrumb have provided Young’s modulus values and fail-ure stresses of 230 and 10 kN m�2, respectively (Scanlonet al., 2000). The modulus values compare favourablywith values for concentrated wheat starch gels subjectedto compression (466 kN m�2, Keetels et al., 1996a), butthe tensile failure stress of bread crumb solids is anorder of magnitude smaller than the compressive failurestress of the starch gel (Keetels, van Vliet, & Walstra,1996c). Larger values for Young’s modulus have gen-erally been obtained for bread crumb solids tested undersmall strain testing conditions, with values ranging from250 kN m�2 (Jagannath, Jayaraman, & Arya, 1999) to80 MN m�2 (Baik & Chinachoti, 2000) reported for theelastic part (E0) of the complex Young’s modulus in adynamic three-point bend test. In the small strain case,the moduli for the starch gels tend to be towards thelower end of the values for their bread counterparts,

with values for E0 ranging from 2 MN m�2 for freshlyprepared starch gels at 49.2% moisture (Rolee & LeMeste, 1997) to 8 MN m�2 for 49% starch gels (Vodo-votz & Chinachoti, 1996), that had been presumablyaged for 1 or 2 days.

5. Relationship between structure and physical texture

of cellular solids

Almost every scientist who has studied the physicaltexture and the cellular structure of bread crumb hasindicated that these two properties are strongly relatedto each other. For example, Kamman (1970) stated thatthe physical and visual texture of bread crumb areinterrelated quality factors that should be considered asa single entity. He speculated that crumb physical tex-ture is largely determined by the character of the grain,e.g. cell wall thickness, cell size and uniformity. Pyler(1988) pointed out that how the crumb feels to thetouch or in the mouth is greatly influenced by the grainor cell structure of the crumb; finer, thin-walled, uni-formly-sized cells yield a softer and more elastic texturethan do coarse, open and thick-walled cell structures.An additional factor to these geometrical characteristicsof the cellular structure is that the mechanical propertiesof bread crumb will be influenced by the mechanicalproperties of the cell wall materials themselves (Chen etal., 1994; Guy & Wren, 1968).

In order to predict mechanical parameters that can beused to characterize bread physical texture (Section 4),physical models must be employed to relate themechanical properties to the structure quantified byimaging techniques (Section 3). The degree of sophisti-cation of the model is to a certain extent determined bythe amount and type of information provided by theimaging system. Therefore, a number of factors thatinfluence the mechanical properties of cellular solids willbe described along with descriptions of specific modelsand/or experiments that have linked these structuralproperties to mechanical properties.

5.1. Measurements of structure related to volumefraction

5.1.1. Bulk densityBulk density, like density, is defined as mass per unit

volume (kg m�3). Bulk density has been used to describethe density of the cellular solid (Attenburrow, Good-band, Taylor, & Lillford, 1989; Barrett, Cardello,Lesher, & Taub, 1994; Gogoi, Alavi, & Rizvi, 2000;Hutchinson, Siodlak, & Smith, 1987; Lee, Lee, & Song,1997; Lourdin, Della Valle, & Colonna, 1995; Rassis,Nussinovitch, & Saguy, 1997; Warburton, Donald, &Smith, 1990, 1992). However, bulk density is usuallyused to describe the packing density of commodities


such as grains, where the space between discrete parti-cles contributes to a reduction in density of the bulkcollection compared to the density of the individualgrains (Lewis, 1990). Given the discussion in Section 2.1on the nature of connectivity of bread crumb, bulk den-sity will not be used to describe the density of bread andother cellular solids. Where the term appears to havebeen used to describe the density of the cellular solid, itwill be discussed simply as density (�), as distinct fromsolid or cell wall density (�s) which is used to define thedensity of the materials comprising the solid phase.

5.1.2. DensityAs for other foamed polymeric materials (Benning,

1969b), density (or its inverse, specific volume, m3 kg�1)has an enormous effect on the mechanical behaviour ofbread crumb (Fig. 7). Because of the large contrast indensities between the two macroscopic phases of breadcrumb, a simple measurement of bread density permitsthe volume fractions to be calculated without recourseto image analysis for determining the distribution of thetwo phases in the bread. Strong relationships betweendensity and various mechanical properties have beenreported for bread and other cellular food products.

Lasztity (1980) and Cornford et al. (1964) speculatedthat changes in bread crumb textural properties (bothelastic and plastic) upon addition of shortening waspartly due to the increase in specific volume. Ponte et al.(1962), who studied crumb firmness and firming rates ofbread, found a strong relationship between compressionforce and specific volume of the bread crumb specimenas it varied across a loaf (r=0.93). Wassermann (1979)also showed that the specific volume of bread crumb(varied by changing proof time) was responsible forchanges in firmness and relative elasticity (ratio of elas-tic recovery to total energy from a hysteresis curve at25% strain). For bread crumb differing in composition(flours of 100% rye, 50% blend of wheat and rye, and

100% wheat), crumb firmness linearly increased whilecrumb elasticity linearly decreased with increasing den-sity. The rate of change in mechanical properties ofbread crumb as a function of density was dependent onbread composition, with rye bread having the highestslope. In contrast though, Barrett et al. (1994) foundthat density alone was not a good predictor of thestrength of extrudates made from various formulationsof maize meal.

Other studies on expanded cereal products have indi-cated that relationships between mechanical parametersand density are not necessarily linear. van Hecke, Allaf,and Bouvier (1995) reported that the bending modulusof crispy extrudates was approximately a cubic functionof their density. Attenburrow et al. (1989) examined therelationship between mechanical properties and struc-ture for sponge cake which had been conditioned todifferent water activities. It was found that both thelogarithm of the modulus and the logarithm of criticalstress were linearly related to the logarithm of density.The suggested relations between density (�), andYoung’s modulus (E) and critical stress (�c) were in thefollowing forms:

E ¼ K1�2 ð1Þ

�c ¼ K2�2 ð2Þ

where K1 and K2 were constants which depended on thewater activity of the sponge cake. They assumed that,for a given water activity, the density of the cell wallmaterials of the sponge cake was invariant over therange of density studied, and so the two relations [Eqs.(1) and (2)] were in agreement with the models of Gib-son and Ashby (1988), discussed later. However, theassumption of invariant solid density is questionablesince studies have shown that the properties of cell wallmaterials, including cell wall density, vary with proces-sing conditions (Bhatnagar & Hanna, 1997; Donald,1994; Warburton et al., 1990).

5.1.3. Relative densityBecause there is variation in cell wall density with

changes in formulation or processing conditions (War-burton et al., 1990; Zghal, Scanlon & Sapirstein, 2001b),then the density of the cellular solid would be expectedto change, and therefore the effect of the structure ofbread on its physical texture would be partiallyobscured. One way of eliminating the effect of cell walldensity changes is to normalize the density of the cel-lular solid (�) according to the density of the material(s)comprising the cell walls (�s). Because the density of thecrumb cells (voids) is negligible (�air�1.2 kg m�3), arelationship between the volume fraction of crumb cells(�c) and the relative density of the bread crumb (�/�s) isapparent:

Fig. 7. Typical compressive stress strain curves for bread crumb cre-

ated by proofing for various times to generate different densities [data

from Chuah and Scanlon (2001)].


� ¼ �c�air þ �s�s

�s�sð3Þ

�s �=�s

1 ¼ �c þ �sð4Þ

�c 1 � �=�sð Þ ð5Þ

where �s is the volume fraction of crumb solids. Thisprocedure confers the advantage of expressing proper-ties of the bread relative to its void fraction (i.e. relativecrumb cell volume). The mechanical performance ofindustrial cellular solids is frequently examined as afunction of void fraction in order to evaluate the effectof changes in formulation or processing conditions(Meinecke & Clark, 1973). The density of the cell wallmaterial for wheat starch bread has been calculated as1240 kg m�3 (Keetels et al., 1996a). Helium pycnometermeasurements of cell wall densities have furnishedhigher values for those of white bread processed undervarious conditions (1430–1624 kg m�3; Zghal et al.,2001b), and for a puffed wheat cereal product (1490 kgm�3; Jones, Chinnaswamy, Tan, & Hanna, 2000).

It has been stated that relative density is the dominantphysical character representing the three-dimensionalstructure of cellular solids (Gibson & Ashby, 1997), andit has been used in many studies, including those ofbiological materials (Kopperdahl & Keaveny, 1998;Lakes, 1993; Shogren, Lawton, Doane, & Tiefenbacher,1998; Warbuton et al., 1990), to quantify the depen-dence of mechanical properties on structure.

5.1.4. Cell wall propertiesIt is to be expected that the mechanical properties of

cellular solids are strongly influenced by the propertiesof cell walls, on the grounds that, for a given relativedensity, more effective and/or more bonding betweenconstituents of the cell wall materials will translate intoa stiffer cellular solid (Ashby, 1989). Benning (1969d)showed that for a given foam density, foams fabricatedfrom resins with a higher molecular weight have differ-ent mechanical properties. This may be an issue in themechanical properties of bread produced from differentwheat cultivars (Scanlon et al., 1997), where differencesin the size of the glutenin macropolymer have beendemonstrated (Gupta, Khan, & MacRitchie, 1993). Inextrusion cooking of maize grits, van Hecke, Allaf, andBouvier (1998) inferrred that the magnitude of cell wallfailure force was related to the molecular size of thestarch molecules comprising the walls.

In view of the thickness of the cell walls in breadcrumb, differences in cell wall properties would beexpected for two reasons. Firstly, differences in starchcontent are expected (Section 2.2.3), with thinner cell

walls having less starch granules, and perhaps impairedmechanical properties (Hug-Iten et al., 1999). Con-versely, if thinner cell walls are associated with greaterstrain hardening of the protein molecules (Dobraszczyk& Roberts, 1994; van Vliet et al., 1992), and theseproperties are carried through to the resulting bread,greater stiffness and strength would be expected (Zghalet al., 2001b). In addition, cell wall properties of breadcrumb will be markedly dependent on moisture contentbecause of its effect on modifying the mechanical prop-erties of the cell walls of cereal-based food foams(Attenburrow et al., 1989; Hutchinson et al., 1989).

5.2. Predicting crumb properties with little or noimaging information

So far, details of the geometrical distribution, or con-nectivity, of the crumb cells within the crumb have notbeen addressed. Information on the volume fractions ofthe individual phases can be obtained from imagingdata (Sapirstein et al., 1994; Zghal et al., 1999), but it ismore readily gained from density measurements [Eqs.(4) and (5)]. The distribution of phases within the crumbmay be irregular (Fig. 1), but statistical homogeneity

Fig. 8. Illustration of statistical homogeneity in bread crumb. Thre-

sholded images are one-eighth sections taken from different regions of

Fig. 1. Exact structures are different, but statistical homogeneity is

apparent.


within the bread crumb is assumed. This refers toinstances where a subregion of crumb can be selectedwhose volume fractions and properties are essentiallythe same as those of the bread crumb specimen as awhole, even though the actual connectivities may bedifferent (Hashin, 1970). An illustration of statisticalhomogeneity in bread crumb is given in Fig. 8. In termsof physical properties, the crumb cell has shear and bulkmoduli that are zero (Watt, Davies, & O’Connell, 1976).Based on extrapolation of modulus values of wheatstarch gels, Keetels et al. (1996a) used a value of 466 kNm�2 for the Young’s modulus of the cell wall phase.Ascribing this value to bread crumb seems reasonableconsidering that bread crumb compressed approxi-mately five-fold has a modulus of 230 kN m�2 (Scanlonet al., 2000).

Using only information on the volume fraction (orrelative density) and the properties of the crumb cellwall material, upper and lower bounds can be predictedfor the properties of the bread crumb by the rule ofmixtures (Christensen, 1982; Hashin, 1970). The expec-tation is that the properties of bread crumb processedby any method or using any ingredients would beexpected to reside between the two bounds (Ahmed &Jones, 1990):

Z ¼ Zs �Zc= Zc ��s þ Zs ��cð Þ Lower Bounds ð6Þ

Z ¼ Zc ��c þ Zs ��s Upper Bounds ð7Þ

where Z is some effective property of the cellular solid(Torquato, 2000). This approach has been used forpredicting the mechanical properties of composite foodmaterials where the second phase (�c) does not havezero values for the bulk and shear moduli (Abdulmola,Hember, Richardson, & Morris, 1996; Aguilera &Stanley, 1999; Clark, Richardson, Ross-Murphy, &Stubbs, 1983). For the case of placing bounds on theYoung’s modulus (E) of bread crumb (Ec=0):

E ¼ 0 Lower Bounds ð8Þ

E ¼ Es ��s Upper Bounds ð9Þ

The obvious problem when applying the model topredicting the mechanical properties of bread is that thelower bounds are zero regardless of how few crumb cellsthere are in the crumb.

Two general criticisms of these bounds are that thebounds are wide, so that accurate prediction of compo-site properties is difficult (Torquato, 2000); for productssuch as bread crumb, where large differences in moduliexist between the two phases, the modulus is very muchover-predicted by the upper bounds (Hashin, 1970).Secondly, the bounds are inappropriate predictors fornon-linear mechanical properties such as strength (Tor-

quato, 2000), a property which is as likely an effectivepredictor of sensory texture as the modulus is (Atten-burrow et al., 1989). For strength, an extreme distribu-tion function is more appropriate (Scanlon & Long,1995; Weibull, 1951), and for this more structuralinformation is required.

Fig. 9 shows how well the bounds cover the distribu-tion of Young’s moduli for bread crumb made fromflour from Canadian Western Red Spring (CWRS)wheat, and processed at two water contents, two sheet-ing conditions and four proof times (Zghal et al., 2001a)and using a value of �s=1532 kg m�3 (Zghal et al.,2001b). Concurring with Hashin (1970), all values fallwell short of the upper bounds predicted by the ruleof mixtures [Eq. (9)]. Much improved upper boundscan be obtained from the Hashin and Shtrikman (1963)bounds, for which prediction of the Young’s modulus ofcomposites containing voids can be expressed as(Christensen, 1993):

Fig. 9. Dependence of relative Young’s modulus (E/Es) on crumb cell

void fraction (φ) for bread made from two water absorptions: 65%

(open symbols) or 60% (closed symbols), and three or five dough

sheeting passes (triangles and stars, respectively). A. Rule of mixtures

lower [R, Eq. (8)] and upper [V, Eq. (9)] bounds, and Hashin-Shtrik-

man lower [HS�, Eq. (8)] and upper [HS+, Eq. (10)] bounds are also

shown. B. Magnification of A at the high void fraction end of the

curve.


E ¼ Es 1 � �cð Þ= 1 þ g��cð Þ½ Upper Bounds ð10Þ

where g=(1+�s) (13�15�s) / 2(7�5�s).

A value of p�1 was assigned as the Poisson’s ratio ofthe cell wall material (�s), although the dependence of gon Poisson’s ratio is not that steep for positive values of�s (Christensen, 1993). The Hashin-Shtrikman boundsare shown on Fig. 9, and, with the exception of one datapoint, they do give a much better description of theYoung’s modulus (firmness) of bread crumb as a func-tion of density than can be achieved from the rule ofmixtures.

5.3. Measurements of structure related to cellularity

The statements on statistical homogeneity in Section5.2 can be taken one step further, to infer that there is aregular repeating unit in the structure of the bread—thecrumb cell and its associated walls (Gibson & Ashby,1988), and that many of these cells are connected toge-ther to fill the volume of the cellular solid. The responseof this cell to loading reflects the response of the solid asa whole (Christensen, 1982), so that analysis of cell

structure is necessary for predicting the mechanicalproperties of the cellular solid. The characteristicdimensions of a cell are shown in Fig. 10 for a cell ofcubic geometry. The influence of these dimensions onthe mechanical properties of cellular food products,especially bread, will be discussed below.

5.3.1. Cell sizeIt is a common perception that the cell size of bread

crumb (or crumb fineness) has a significant effect on itsphysical texture (Kamman, 1970; Pyler, 1988). How-ever, Gibson and Ashby (1997) remarked that themechanical properties of cellular solids are weaklydependent on cell size per se, and that the distribution ofcell sizes has a greater influence. For bread crumb,Zghal et al. (2001b) found that crumb cell size measuredby digital image analysis was negatively correlated(P<0.05) with both Young’s modulus and failure stressof the crumb, confirming for a high moisture cerealproduct, the inverse relationship that had been observedbetween bending modulus and average cell size forcrispy flat breads (van Hecke et al., 1995). Although cellsize distribution was expected to have a greater effectthan cell size, a measure of cell size uniformity was not

Fig. 10. Dimensions for unit cells of cellular solids (drawn as cubes, so that l=h). A. Open cell. B. Closed cell, where wall thickness is equal throughout. C.

Side view of closed cell where solid phase is distributed unevenly, so that wall thickness is thinner in faces than in edges of cell. D. Cell that is likely typical

for bread crumb, where some faces are open and some are closed, and solid is distributed unevenly in cell walls. Adapted from Gibson and Ashby (1982).


significantly related to mechanical properties of breadcrumb (Zghal et al., 2001b). Barrett et al. (1994) foundthat plateau and peak stresses were strongly related(r250.91) to a combined effect of density and mean cellarea in corn meal extrudates. The values of these stres-ses decreased as cell size increased at a constant density.They noted that the effect of mean cell area on thestrength of the extrudate was not obvious because ofother changes that occurred in structure, such as chan-ges in cell wall thickness and shape. In recent experi-ments on extrudates expanded by supercritical CO2,Gogoi et al. (2000) observed that cell size could notpredict strength well (r2>0.8) for all protein additives,but that density alone could.

5.3.2. Cell wall dimensionsCell wall thickness, cell wall thickness distribution,

and the presence of defects in cell walls have beenshown to affect the overall mechanical properties ofcellular solids (Gibson & Ashby, 1997). Thicker cellwalls were anticipated to impart greater mechanicalstrength because cell wall thickness is associated withhigher density (Barrett et al., 1994). However, when theeffect of cell wall thickness is examined at constantdensity, thinner cell walls infer finer structure whichcould result in greater mechanical strength. Some evi-dence for this was seen for baked starch foams (Shogrenet al., 1998) and for bread crumb, where negative cor-relations between mean cell wall thickness and bothYoung’s modulus and fracture stress was reported(Zghal et al., 2001b). Distance to failure, which is ameasure of the flexibility of the starch foams (Shogrenet al., 1998), was thought to depend on cell wall dimen-sions, since thinner cell walls could flex more easilywithout breaking than thicker ones, and therefore resultin greater deflection at break.

Gibson and Ashby (1988) provided a more criticalanalysis of mechanical properties and cell wall dimen-sions by combining ‘‘simple mechanics with scalingideas’’ (p. 121) for foams where cell wall thicknesses (te

and tf) were small relative to cell size. They (Gibson &Ashby, 1982) showed that the Young’s modulus of thefoam (E) was related to the cell wall dimensions inFig. 10A and B:

A : E ¼ Es �c� t4e=l

4� �

open cells; tf ¼ 0ð Þ ð11Þ

B : E ¼ Es �c� t3f =l

3� �

closed cells; tf ¼ teð Þ ð12Þ

where the values of the constants c are not equal in Eqs.(11) and (12), and they also depend on cell shape.

The description of crumb cell wall formation given inSection 2 implies that a strict demarcation betweencrumb solid material being uniformly distributed acrossthe faces or exclusively confined to the edges is unlikely

to be the case for crumb cell walls. Therefore, Gibsonand Ashby (1982) also gave a relationship for closedcells when cell wall material was distributed unevenly(Fig. 10C):

C : E ¼ Es �c� t4e þ t3

f �l� �

=l4 closed cellsð Þ ð13Þ

Because the weight of the bread crumb is proportionalto cell wall thickness while its volume is proportional tocell wall length, the three expressions [Eqs. (11), (12)and (13)] for crumb modulus can also be expressed asfunctions of relative density (Gibson & Ashby, 1982,1988) by using the relationships:

�=�s / t=lð Þ2 open-cells foams; t ¼ teð Þ ð14Þ

�=�s / t=lð Þ closed cellfoams; t ¼ tf ¼ teð Þ ð15Þ

�=�s / t2e þ tf l

� �=l2 ð16Þ

so that for Eqs. (14) and (15) (the two simpler cases),Young’s modulus is given by:

E=Es / �=�sð Þm

ð17Þ

where the power law index, m, depends on the type offoam. The constant of proportionality in Eq. (17) isclose to 1, based on analyses of structure for regularshaped cells of foams (Gibson & Ashby, 1988). Experi-mental studies on engineering foams (Gibson & Ashby,1988) and wheat starch bread crumb (Keetels et al.,1996a) have confirmed that the constant of proportion-ality has a value close to unity. Therefore, a value forYoung’s modulus of the cell wall material of breadcrumb can be obtained by extrapolating crumb modulusvalues to �/�s=1.

On the basis of analysis of cell wall dimensions (Gib-son & Ashby, 1982), a similar scaling relationship is alsoexpected between relative density and a critical stressvalue (�c), e.g. �c in Fig. 6 or the peak or plateau stres-ses measured by Barrett et al. (1994). For bread crumb,which does not collapse in a brittle manner:

�c=�y / �=�sð Þn

ð18Þ

where �y is the yield stress of the crumb cell wall mate-rial. In general terms, the exponent n and the constantof proportionality depend on the mode of loading andthe physical nature of the collapse phenomenon (Gibson& Ashby, 1988), and for closed cells a correction factormay also have to be added to account for the effect offluid pressure.


Despite the difficulty in assigning a unit cell for thecellular structure of bread crumb, Keetels et al. (1996a)have indicated that the theoretical relationships abovecan still be used to relate the microstructure to theoverall shape of the compressive stress-strain curve. Intensile tests, Zghal et al. (2001b) showed that theYoung’s modulus and fracture stress of bread crumbwere well fitted to the power law model with r2 valuesbeing on average 0.79 and 0.77, respectively. Their fitfor bread crumb made from a medium strength flourusing different processing conditions is shown in Fig. 11.The value of Es at 468 kN m�2 concurs with the valueobtained for starch bread by Keetels et al. (1996a).However, the values of Es for other flours and bakingabsorptions covered a considerable range (132–851 kNm�2), depending on water absorption and flour type.The power law indices for all wheat classes (m valuesranged from 0.98 to 1.58 and n values from 0.54 to 0.96)were substantially lower than the theoretical values lis-ted for Eqs. (17) and (18) (Zghal et al., 2001b). Lowvalues for the exponents m and n were also reported byShogren et al. (1998), for baked starch foams (r2=0.99)subjected to tensile testing, and for extruded starchfoams of varying amylose content (r2>0.57; Lourdin etal., 1995). Hutchinson et al. (1987) found a strong rela-tionship between mechanical properties (from compres-sion, tension and flexure tests) and the density ofextruded maize using Eqs. (17) and (18). However, theyalso found that the power law indices m and n wereintermediate between the expected values for open andclosed cells, as did Gogoi et al. (2000) for the compres-sive modulus of starch/protein extrudates expanded bysupercritical CO2 rather than steam (r2=0.87). A dis-cussion of the significance of the value for the exponentsm and n in terms of cell structure and the expectedmodes of deformation of the cell walls for brittle starchextrudates has been given by Smith (1992) and War-

burton et al. (1992). The manner in which the liquidphase distributes itself in the cell walls during proofingand baking is expected to affect the physical texture ofthe crumb, in an analogous fashion to how distributionof solid within the cell has an effect on the mechanicalperformance of engineering foams (Miyoshi et al., 1999;Simone & Gibson, 1998).

Another plausible explanation to account for the lowvalues of m and n for bread is that the mechanical per-formance of the cell wall has been enhanced by strainhardening which occurred as cell walls were stretchedduring proofing and baking (Dobraszczyk & Roberts,1994; van Vliet et al., 1992). When a strain hardeningfactor was incorporated into Eqs. (17) and (18) withexponents of m=2 and n=1 (tensile testing of open cellfoams) slight improvements in the fit were obtained(Zghal et al., 2001b). However, of more significance wasthe finding that the range of cell wall moduli and yieldstresses for the solid phase of bread crumb made fromdifferent wheat classes was considerably narrowed tomore realistic values (Keetels et al., 1996c). In addition,the strain hardening exponents for breads made fromdifferent wheat classes were ranked essentially accordingto dough strength, concurring with experimental studiesof strain-hardening in doughs (Wikstrom & Bohlin,1999). Ascribing predictive capacity to the model ofZghal et al. (2001b) is premature, but their work doesimply that mechanical events occurring in the dough dopersist to affect the properties of the bread crumb.

5.3.3. Missing cell wallsDue to the nature by which bread crumb structure

arises, defects in the cell walls [missing (due to coales-cence) or ruptured cell walls] and variability in cell wallthickness distribution are factors that must be con-sidered in structural analyses. From numerical simula-tions of the stress-strain behaviour of periodic and non-periodic honeycombs, it was shown that both Young’smodulus and compressive strength (Silva & Gibson,1997) substantially decreased with increasing numbersof missing cell walls. The loss of 5% of the cell wallsresulted in over a 30% decrease in modulus andstrength, and the removal of 35% of cell walls com-pletely eroded both modulus and strength (Silva &Gibson, 1997). The reason ascribed to the severe degra-dation in mechanical properties while still at a fairlyhigh volume fraction of solid was that a plane of dis-connectivity arose in the honeycomb structure, thuspreventing stress transmission. By considering the changein crumb cell volume fraction relative to the number ofcells observed at the cut crumb surface, Zghal et al.(2001b) calculated the number of missing cell walls inbreads made at different proofing times, and incorpo-rated its effect into a model of crumb mechanical prop-erties. However, their analysis did not account fordifferences in spatial distribution of these missing cell

Fig. 11. Young’s modulus as a function of relative density for bread

crumb made from a medium strength flour (Canada Prairie Spring wheat)

at four proof times, and three (~) and five (?) sheeting passes. Data from

Zghal et al. (2001a). Error bars represent 95% confidence limits.


walls, and it has been shown that interaction betweenstress fields generated by two closely spaced defects willdegrade strength more than the effect associated withjust the loss of solid material (Guo & Gibson, 1999).Ingredients such as emulsifiers tend to lower the numberof missing cell walls created during processing (Brooker,1996; Schramm & Wassmuth, 1994), and hence affectthe physical texture in the resulting crumb. In brittleextrudates to which glycerol monostearate had beenadded, van Hecke et al. (1998) observed a greater num-ber of structural ruptures during texture testing, a find-ing consistent with the emulsifier helping to retain agreater number of cell walls in the product.

The effect of uniformity in the distribution of cell wallthicknesses of bread crumb was also considered byZghal et al. (2001b). Uniformity was positively corre-lated with both Young’s modulus and fracture stress(r250.94), whereas they found the effect of missing cellwalls alone was not statistically significant.

5.3.4. AnisotropyGibson and Ashby (1997) described anisotropy of

cellular solids as the tendency of cells to be elongated orflattened or to have walls of unequal thickness. Aniso-tropy was classified into two categories which are direc-tion-dependent: structural anisotropy and materialanisotropy. The former is a measure of cell shape, whilethe latter refers to the properties of the cell walls. Basedon the likely mode of creation of the crumb cells inbread crumb (Section 2), it is expected that both aniso-tropies will occur in bread crumb. For cells with onedimension longer than the other two, structural aniso-tropy is characterized by a shape anisotropy ratio (R),measured as the ratio of the largest cell dimension to thesmallest (Gibson & Ashby, 1997). On the other hand,where cells sizes differ in all three dimensions, twovalues of R are used to characterize the structural ani-sotropy. On the basis of tomographic images of aproofing dough (Whitworth & Alava, 1999), it could beargued that by the end of final proof, axisymmetric struc-ture has been established. Therefore, the bread crumbstructure that emerges from the dough should displaysimilar anisotropy, with cells elongated parallel to thelong axis of the loaf, so that only one R value is required.

In an investigation of bread crumb firmness measuredin compression, Hibberd and Parker (1985) showed thatthere was a highly significant dependence of crumbmechanical properties on the direction of measurement(Section 4.2.1). They attributed the development of ani-sotropy in the crumb to the moulding operations. Simi-lar effects of processing on cell shape have been reportedby Warburton et al. (1992) for extrudates where thelargest cells were aligned parallel to the direction ofextrusion, and for supercritical fluid expanded extru-dates whose compressive modulus was strongly depen-dent on how cell shape was altered by post-extrusion

drying (Gogoi et al., 2000). Persaud et al. (1990) useddynamic stress–strain measurements to characterize theproperties of freshly baked and aged bread crumb, butfound that the shear storage modulus G0 was the samein all three directions, and therefore concluded that thebread crumb taken from the centre of loaves lackedanisotropy. They reconciled the difference between theirresults and those of Hibberd and Parker (1985) to dif-ferences in the mode of baking which would affect cellstructure. However, another likely reason is that in ani-sotropic cellular structures, the shear modulus is muchless sensitive to anisotropy than Young’s modulus(Gibson & Ashby, 1997), so that the effect of cellularanisotropy in bread crumb may have been undetected inthe experiments of Persaud et al. (1990).

6. Conclusions

As for other composite cellular solids, density exerts astrong influence on the mechanical properties of breadcrumb. With information on the physical properties ofthe solid phase of bread crumb, it is possible from aknowledge of bread crumb density to define a range ofmodulus values which the bread crumb will definitelypossess. Quantification of additional structural infor-mation by image analysis will permit improvements inpredictive capacity. To take better advantage of modelsused for predicting the physical properties of industrialand biomedical cellular solids from their structure, pre-cise and systematic measurements of the mechanicalproperties of breads created from various raw materialsand processing conditions is advocated.

Acknowledgements

We are grateful for research funding from NSERC,and we also thank Dr. Martin Whitworth of Campdenand Chorleywood Food Research Association for a digi-tal image of CBP bread crumb, Dr. Grant Campbell of theSatake Centre for Grain Process Engineering (UMIST,Manchester) for his data on dough density, and Dr.Harry Sapirstein and Mr. Randy Roller of the Universityof Manitoba for data that was used to create Fig. 4.

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