OATAO is an open access repository that collects the work of Toulouse
researchers and makes it freely available over the web where possible
Any correspondence concerning this service should be sent
to the repository administrator:
tech-oatao@listes-diff.inp-toulouse.fr
This is an author’s version published in: http://oatao.univ-toulouse.fr/20615
To cite this version:
Ostvar, Sassan and Iltis, Gabriel and Davit, Yohan
and Schülter, Steffen and Andersson, Linéa and Wood,
Brian D. and Wildenschild, Dorthe Investigating the
Influence of Flow Rate on Biofilm Growth in Three
Dimensions using
Microimaging.
(20
18) Advances
in Water Resources, 13. pp. 1 - 13. ISSN 0309-1708
Official URL:
http://dx.doi.org/
10.1016/j.advwatres.2018.03.018
dimensions
using
microimaging
Sassan
Ostvar
a,
Gabriel
Iltis
a,
Yohan
Davit
b,
Steffen
Schlüter
c,
Linnéa
Andersson
a,
Brian
D.
Wood
a,
Dorthe
Wildenschild
a,∗a School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis, Oregon, USA b Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, Toulouse, France c Department of Soil Physics, Helmholtz-Centre for Environmental Research - UFZ, Halle, Germany
a
r
t
i
c
l
e
i
n
f
o
Keywords:Biofilms
Granular porous media X-ray computed microtomography Image processing
Statistical learning Fluid phase topology
a
b
s
t
r
a
c
t
WeexplorehowX-raycomputedmicrotomographycanbeusedtogeneratehighly-resolved3Dbiofilmdatasets onlengthscalesthatspanmultipleporebodies.Thedataisintegratedintoastudyoftheeffectsofflowrate onthree-dimensionalgrowthofbiofilminporousmedia.Threeflowrateswereinvestigatedinmodel packed-bedcolumns.Biofilmgrowthwasmonitoredduringan11-daygrowthperiodusingacombinationofdifferential pressureandeffluentdissolvedoxygenmeasurements.Attheendofthegrowthperiod,allcolumnswerescanned usingX-raycomputedmicrotomographyandabariumsulfate-basedcontrastagent.Theresultingimageswere preparedforquantitativeanalysisusinganovelimageprocessingworkflowthatwastailoredtothisspecific system.Thereductioninpermeabilityduetobiofilmgrowthwasstudiedusingbothtransducer-basedpressure dropmeasurementsandimage-basedcalculationsusingtheKozeny–Carmanmodel.Inaddition,asetofstructural measuresrelatedtothespatialdistributionofbiofilmswerecomputedandanalyzedforthedifferentflowrates. Wegenerallyobserved1to2ordersofmagnitudedecreaseinpermeabilityasaresultofbiocloggingforall columns(i.e,acrossflowrates).Thegreatestaveragepermeabilityandporosityreductionwasobservedforthe intermediateflowrate(4.5ml/h).Acombinationofresultsfromdifferentmeasurementsallsuggestthatbiofilm growthwasoxygenlimitedatthelowestflowrate,andaffectedbyshearstressesatthehighestflowrate.We hypothesizethattheinterplaybetweenthesetwofactorsdrivesthespatialdistributionandquantityofbiofilm growthintheclassofporousmediastudiedhere.Ourapproachopensthewaytomoresystematicstudiesof thestructure-functionrelationshipsinvolvedinbiofilmgrowthinporousmediaandtheimpactthatsuchgrowth mayhaveonphysicalpropertiessuchashydraulicconductivity.
1. Introduction
The interaction of hydrodynamics and biofilm growth in media withtortuous geometriesisof great scientificinterestbecauseof its prevalencein manynaturalandengineeredsystems(Drescheretal., 2013).Asexamples,biofilmgrowthinporousmediahasbeenboth di-rectlyobservedandindirectlyhypothesized(withsubstantial support-ingevidence) in a widevariety of natural andengineered systems. These include examples such asanaerobic reactors (e.g. Young and
Dahab,1983),microbially-enhancedoilrecovery(e.g.Armstrongand
Wildenschild,2012;Sen,2008),micromodelexperiments(e.g.Kimand Fogler,2000;StewartandFogler,2001),laboratoryporousmedia ex-periments(e.g.Vogtetal.,2013),andslowsandfilterbeds(e.g.Lietal., 2013).Althoughthereareongoingdiscussionsregardingtheubiquityof biofilms(BaveyeandDarnault,2017;Coyteetal.,2017),thesestudies
∗Correspondingauthor.
E-mailaddress:dorthe@engr.orst.edu(D.Wildenschild).
offersignificant,andoftendirect,evidencethatbiofilmformationin porousmediaisanimportantcomponentformanyprocessesof rele-vanceandinterest.
Innaturalandsyntheticporousmedia,biofilmgrowthatthepore scaleaffectsvarioustransportprocessesbyalteringthestructureof in-terfaces,connectivityoftheporespace,andbulkgeometricproperties ofthemedium(Baveyeetal.,1998;Cunninghametal.,1991;Drescher etal.,2013;Rittmann,1993).Inturn,cellulargrowthandmesoscale structuralevolutionofbiofilmsarehighlyinterconnectedwithvarious aspectsoftransportincludingshearandmasstransfer.Non-destructive imagingofbiofilmsisessential tounderstandingthephysicsof these processesandtheirbroaderimpactsondesign,control,andprediction. Indisciplinesthatareconcernedwithnaturalporousmedia(e.g. hy-drology,petroleumengineering),theabilitytovisualizebiofilmgrowth underflowonthescaleofmillimeterstometershasbeenofgreatinterest
Nomenclature
𝜑 porosity
𝜌 fluiddensity
vs≡vz (stream-wise)superficial(Darcy)velocity D poreradius(≡characteristiclengthscale)
𝜇 fluidviscosity
Re Reynoldsnumber
Q volumetricflowrate
A cross-sectionalarea
𝜅zz stream-wisecomponentofthepermeabilitytensor
p hydrodynamicpressure
g accelerationduetogravity
K columnhydraulicconductivity
Φ Hubbert’spotential(hydraulichead)
L columnlength
ΔP netpressuredifferenceacrosscolumn
𝜏 tortuosity
interfacialareatovolumeratio
𝛽 constantintheKozeny–Carmanmodel
I totalnumberofevaluatedimages
N totalnumberofvoxelsevaluatedatcoordinate x
Π setofallpairsofneighboringvoxels 𝑐(x ) classlabelofvoxelatpoint x
𝜇c,𝜆 classmeaninimage𝜆
𝜎2 classvarianceinimage𝜆 𝑔𝑖(x ) grayvalueofvoxelx inimagei
𝜒 Eulercharacteristic
numberofisolatedobjectsinamaterialofinterest numberof redundant connectionswithin all material
clusters
numberofcavitiesinamaterialofinterest d𝛼 averageporediameterinphase𝛼
e𝛼 averagedistancewithinphase𝛼
CI theconnectivityindex
PSI theporesizeindex SDI thesoliddistanceindex
(e.g. Thullner,2010; Yarwoodet al., 2002).Visualizationis gaining evenmoresignificancewiththeincreasingcomplexityandfidelityof themathematicalandcomputationalapproachestomodeling biofilm growthin porousmedia (e.g.vonderSchulenburgetal.,2009).The challengesassociatedwithnon-intrusivevisualizationof3Dsystems of-tenforcesdirectcomparisonbetweenmodelsandexperimentstorely onbulk(aggregate)laboratoryorfieldmeasurements;i.e.evaluations onscaleswherepore-scale(structural)informationdetrimentalto trans-portislosttotheaveraginginherenttomeasurements(Thullner,2010). MagneticResonanceMicroscopy(MRM)andNuclearMagnetic Res-onanceimaging(NMR)havebeensuccessfullyappliedtoelucidatethe globalstructureofbiofilmsinporousmediaandporefluidvelocitiesin mediaalteredbymicrobialgrowth(Manzetal.,2003;Seymouretal., 2004; 2007),albeit with some resolution limitations. Confocal laser scanningmicroscopy(CLSM),andmorerecentlyopticalcoherence to-mography(OCT),havebeensuccessfullyappliedtothevisualizationof the3Dstructureofbiofilmsonsmallerscaleswithhigherresolutions (Davitetal.,2013;Dreszeretal.,2014;NeuandLawrence,2015; Wag-neretal.,2010;Xietal.,2006).Bothmethodsenabletemporalstudies ofgrowthinflowenvironments,andprovidehighlyresolved reproduc-tionsoftheinternalstructureofthebiofilmmatrix.Apopularapproach todirectvisualizationofbiofilmstructureinporousmediaatthepore scalehasbeentoadoptthesetechniquestostudygrowthinoptically transparent(Leisetal.,2005),2Dandpseudo-3Dmicro-models(e.g. Beyenaletal.,2004;KimandFogler,2000;RodríguezandBishop,2007; Stoodleyetal.,1999).
Alimitationinextendingthismethodologytostudybiomass forma-tionin3Dporousmediaisthatexperimentalsystemsmustbeoptically transparent,smallenoughtofitontothemicroscopestage,andinthe caseofCLSM,thinenoughtofitwithinthefocalrangeofthedevice. Conversely,3Dporoussystemsareopaqueanddeep.Whetherornot theconclusionsdrawnfor2Dsystemscanbeextendedto3Disan unan-sweredquestion.Topologically,thetwoarenotequivalent(e.g., diffu-sionsin2-and3-dimensionsarefundamentallydifferent),soonewould notexpect2-dimensionalexperimentstocapturetherangeofphysical behaviors.Thus,theliterature’sprevailinganswertothisquestionseems tobenegative(e.g.seethediscussionbyBaveye,2010;Thullner,2010). X-raycomputedmicrotomography(CMT)isemergingasan alterna-tivethatenablesvisualizationofbiofilmsin3Dinopaquemedia(Davit etal., 2011;Iltis etal.,2011; WildenschildandSheppard,2013) on theporescale. Thoughstillin itsinfancy,themethodwasoriginally developedandexploredusingbothpolychromatic(Davitetal.,2011) andmonochromaticsynchrotron-basedsystems(Iltis,2013;Iltisetal., 2011).Userscanexpectvoxelresolutionsontheorderof1–2microns tobeeasilyachieved.Thetechniquereliesontheuseofcontrastagents tofacilitatetheadsorption-baseddetectionofdifferentphaseswithinan opaquesampleusingX-rays.Centraltothemethodiscreatingaphysical mechanismthat,throughtheuseofadvancedimageprocessing tech-niques,allowfordifferentiationbetweenthefluidandbiofilmphases, thenaturalattenuation(photoncross-section)ofwhicharealmost iden-tical.
Useofdifferentcontrastagents,addedtotheaqueousphase,such as silver-coated hollowmicrospheres (Iltis etal., 2011), barium sul-fatesuspensions(Davitetal.,2011;Iltis,2013),and1-chloronaphtalene (Ivankovicetal.,2017;duRoscoatetal.,2014)haveshownpromise. Similarly,addingFeSO4asacontrastagenttothebiofilmphase,and usingthefreespacepropagationofX-raystobringoutadditional re-fractiveeffects,Carrel etal.(2017)werealsoabletoimagebiofilms inopaqueporousmedia.ThelatterstudycomparedtheFeSO4tothe BaSO4methodandfounddifferencesintheamountofbiofilmimaged, withasignificantlylargeramountofbiofilmidentifiedusingtheFeSO4 method.The authorspointed out three possible reasons for the dis-crepancy;(i)partialvolumeeffects(eliminatedfromconsideration);(ii) uncertaintyrelatedtothesegmentation(causedbythesignificant het-erogeneityofthebiofilmphaseandpoorcontrastofsaidphase);and (iii)interactionbetweentheBaSO4andthebiofilm(causingsuspended biomassandlooselyattachedcomponentsofthebiofilmtobewashed outofthecolumns).
Thepotentialfordetachmentofbiofilmduringadditionofadenser andmoreviscous(aqueousphase)contrastagent hasbeendiscussed
by Davit et al.(2011) and duRoscoat etal. (2014). In a thorough
studyoftheproblem,Ivankovicetal.(2017)foundthatthiseffectcan be eliminatedbyusingsmallerbeads(intheircase,lessthan2mm) andbymakingmeasurementsafterlongerperiodsofbiofilmgrowth (>7days)suchthatamorecompactandtightlyattachedbiofilmwas formed.Thisallowedforreliablestudiesonbiofilmsthatpresented sim-ilarandreproduciblespatialstructureandallowedforquantitative eval-uationofanumberofdifferentenvironmentalvariables.Intheirstudy, growthperiodsof lessthan3days,andlargerporesizes,resultedin lessresilientbiofilms(exhibitingstreamersandotherweaklyattached components)thatmaybesubjecttodetachmentshearbyamore vis-couscontrastagent(suchasBaSO4or1-chloronaphtalene).Forthe 1-chloronaphtalene(CN)anadditionalchallengewascausedbytheoily natureofthecontrastagent,whichcausedpendularringsofCNtobe leftbehindatbeadcontacts.
Theexactgrowthperiodandporesizethatwillproducerepeatable experimentswillvarysomewhatwithorganism,nutrientsupply,flow rate(allfactorscontributingtotheproductionof moreorlessdense biofilms),andtheviscosityoftheinjectedcontrastagent(ifrelevant). Thepaststudiesusingaqueousphasecontrastagentsserveas promis-ingproofoftheconceptaslongastheriskofviscousinteractionwith thebiofilmisconsideredinthedesignoftheexperiments.Whilethere
is lessrisk ofdetachment usinga contrast agentin thebiofilmitself (Carreletal.,2017),theresultingweakcontrastbetweenthevarious phasesmakesreliableandobjectivequantitativeevaluationdifficult.
Inthisstudy,wepresentasystematicstudyonthecorrespondence betweenphysicalquantitiesderivedfromCTdataandphysical measure-mentsofbiofilmgrowth;suchacomparisonhasyettobereportedin theliterature.Ourdataconsistsofduplicatecolumnsgrownfor11days toensureadenseandresilientbiofilm.Theresultingimagehistograms exhibitdistinctseparationoftheintensitypeaks(indicativeofeffective phaseseparation)andweuseadvancedimageprocessingmethodsto allowforobjectivemeasurementsofanumberofbiofilmfeaturesasa functionofReynoldsnumber(Re).
Whenpossible,wecross-validatetheresultsobtainedvia microim-ageanalysiswiththoseobtainedviadirectbulkmeasurements. Numer-ousstudiesconductedonbioclogginginporousmediaundervarious conditionshavereportedsignificantreductionsinhydraulic conductiv-ity,oftenupto2–3ordersofmagnitudeormore(Bielefeldtetal.,2002; Cunninghametal.,1991;SeifertandEngesgaard,2007;Thullner,2010;
VandevivereandBaveye,1992).Duemainlytolimitationsin
measur-ingorimagingthespatialdistributionofbiomass,however,onlyafew reportshaveattemptedtoassociatechangesinporemorphologywith changesinhydraulicconductivityin 3D,mostlyindirectlyorvia de-structivesampling.Anumberofauthorshaveobservedthatamajority ofthebiomassandassociatedcloggingoccurredwithinthefirst sev-eralcentimetersoftheexperimentalapparatus(e.g.Seifertand Enges-gaard,2007).Othershavearguedthatbiocloggingshouldbeattributed primarilytoblockageofporethroatsbybiomassasopposedtouniform continuousfilmsonsolidsurfaces(e.g.Vandevivereetal.,1995).
2. Methods
BybuildingontheworkofDavitetal.(2011),westudyflowrates thatspanthreeordersofmagnitude(correspondingtoinitialpore-scale Reof0.1,1.0,and10),coveringcreepingtomildlylaminarflows.We areparticularlyinterestedincharacterizingtheglobalbiofilmstructure grownunderthestipulatedflowconditionsandtracingthesevariations tobulkmeasurements.Theworkintroducesasimpleanalysisofbiofilm growthwithinopaqueporousmediabasedon3Dstructuralmeasures alongwithcorrelationto(i)bulkpressuredropmeasurementsand(ii) dissolvedoxygenconsumptiontoevaluatepotentialnutrientlimitations impartedbytheappliedflowrates.Ouranalysisreliesonanovelimage processingworkflowthataddressessomeofthelimitationsassociated withinhomogeneousdistributionofthecontrastagentintheporespace. 2.1. Modelporousmedium
Packedbeadcolumnreactorsmeasuring6.3mmindiameter,42mm inlength,witha25mmclearwindowwereconstructedof polycarbon-atetubing.Theporousmediumconsistedofsoda-limesilicaglassbeads, withparticlediameterwithintherange1.4–1.7mm,andspecific grav-ityof2.5.Atotalof6growthreactorswereusedinthisstudy,sothat therewereduplicatecolumnsexaminedateachflowrate.Initialcolumn porositiesweremeasuredgravimetricallypriortotheexperimentsand initialflowtestingwasconductedtomeasurethehydraulicconductivity ofthemodelsasdescribedbelow.
2.2. Microbialspecies
The bacterium used in this study is Shewanella oneidensisMR-1; a metal-reducingstrain originally isolatedfrom sediment from Lake Oneida in New York. S. oneidensis MR-1is a gram-negative, highly piliated, polarly flagellated, facultative anaerobe capable of dissim-ilatory metal reductionand biofilm formation (Majors et al., 2005;
Venkateswaranet al., 1999).The bacterium is motile; the presence
ofpiliarecriticaltoinitialadhesionandtheflagellahavebeen iden-tifiedasbeing criticalfordevelopment of effectivebiofilmstructure
(Thormannet al., 2004).The bacterium hasalso beenshown to be
motileinresponsetolowoxygentensions(Thormannetal.,2005).This strainhasbeenusedsuccessfullyinprevious biofilmimagingstudies conductedbyourgroup(Iltisetal.,2011).
2.3. Growthmediaandconditions
Inoculaweregrownfromfrozenstock fortwogrowthcycles. Ini-tially,frozen stock wasthawed and0.5mLstockculture was added to30mLsterile100%(30g/L)TrypticSoyBroth(TSB).Batchcultures weregrownonanincubatedshakertableat250rpmand30°Cfor20h atwhichpointthesecondgrowthcyclewasstartedbyadding1mLof batchculturefromthefirstgrowthcycleto30mLfresh,sterile100% TSBgrowthmedia.Batchcultureswerethenincubatedforanother20h cycle.Attheconclusionofthesecondgrowthcycle,batchcultureswere centrifugedat6000rpmfor10min,thesupernatantwaspouredoff,and thecellpelletswereresuspendedin5mL100%TSB(30g/L)growth me-diaforcolumninoculation.
Allcolumngrowthreactorsandtubingweresterilizedpriorto inoc-ulationbyflushinga90%ethanolsolutionthroughthetestapparatus for30min,atwhichpointagrowthmediaflushcommencedtoensure thatallethanolwasremovedfromthesystempriortoinoculation.The sterile10%TSB-saturatedcolumnsweretheninjectedwith1mLofthe concentratedcellinoculum.A24hnoflowperiodwasallowedto pro-motebiofilmnucleation,afterwhichflowofsterileoxygenatedgrowth mediawasstartedattheprescribedflowrates.
Inoculafortheinitialgrowthperiodwerepreparedin100%(30g/L) trypticsoybroth(TSB)solutions.Themediumwasdiluteddownto10% (3g/L)fortheflowexperiments.Allgrowthmediaweresterilizedprior toinjection,andcontinuouslyaeratedusing0.22µmfilteredambient air.Aconsistentlyoxygen-saturatedinjectionwithanaverageinfluent O2concentrationof8.05 ± 0.29(mg/L)wasmaintainedintheflow experiments.
Threeflowratesinthecreepingandmildlylaminarregimeswere targetedforinvestigation.ThecorrespondinginitialRewere0.1,1and 10,wheretheReisevaluatedforapackedbedusing(Gunjaletal.,2005) 𝑅𝑒= 1
(1−𝜑) 𝜌 𝑣𝑠𝐷
𝜇 (1)
Here,𝜌 (g/mL)isthedensityofthefluidphase,D(cm)isacharacteristic porelengthfortheporousmedium,takentobetheaveragegrainsize; 𝜇 (g/cm/h)isthedynamicviscosityofthefluidphase;and𝜑isthebulk porosity;andvs(cm/h)isthesuperficial(Darcy)velocitydefinedas 𝑣𝑠=
𝑄
𝐴 (2)
whereQ(mL/h)isthefluidflowrateA(cm2)isthecross-sectionalarea withouttheporousmedium.Notethat𝜑changesduringthecourseof theexperimentssotheabovevaluesrepresentReynoldsnumbersatthe onsetofgrowth.Forthemodelsystemsusedinthisstudy,thesevalues correspondtoflowratesof4.5,45,and450(mL/h).Thesevaluesare referredtoasthelowest,intermediate,andhighestflowratesthroughout thetext.
Continuousflowwasprovidedtoeach columngrowthreactor us-ingcontinuous-cyclesyringepumps.Checkvalveswereusedtoensure that flow throughthe reactor columnswas always unidirectional.A schematicoftheexperimentalsetupisprovidedinFig.1(a).Growth mediareservoirswerereplacedatapproximately36hintervals,andall influentlineswerereplacedeverytwodaystominimizebiofilmgrowth upstreamoftheexperimentalcolumns.Biofilmgrowthwasallowedto continueunderconstantflowconditionsfor11days,atwhichpointthe columnsweredisconnectedandpreparedforimaging.
2.4. Differentialpressuremeasurement
Differentialpressuretransducers(HoneywellSensingandControl, 24PCSeries, ColumbusOH,USA) wereaffixedtoeach experimental
Fig.1.Schematicforexperimentalflowapparatus(a).Schematicforsynchrotron-basedX-raymicrotomographicimagingofthe3Dopaquesamples(b).Sample cross-sectionalgrey-scaleimageofacolumnafterbiofilmgrowth(darkcirculargreyareasareglassbeads)(c).Thesamesampleaftersegmentationusingthemodified MarkovRandomFieldalgorithm(blue=glassbeads,red=biofilm,andyellow=fluid)(d).3Dreconstructionofasegmentedporousmediumafterbiofilmgrowth at𝑅𝑒=10(e)(darkgray=beads,blue=biofilm).Thedashedrectangularareain(d)isanalyzedindetailinFig.2.(Forinterpretationofthereferencestocolour inthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
columnatthecolumnentranceandexitinordertoallowfor measure-mentofdifferentialpressureacrosseachcolumnlength.Continuous dif-ferentialpressuremeasurementswerecollectedbyanautomateddata acquisitionsystem(PersonalDAQ50,MeasurementComputingCorp., Norton,MA).
2.5. Dissolvedoxygenmeasurement
Periodicmeasurementsof dissolvedoxygen(DO)wereperformed ontheinfluentandeffluentsidesofeachcolumnforthedurationofthe biofilmgrowthphaseoftheexperiment.EffluentDOwasmeasured us-ingflow-throughoxygenmicroprobes(Model16-730,Microelectrodes Inc.,BeadfordNH,USA).InfluentDOmeasurementsweremadeusing aseparateprobe(Symphony,VWRInternational)onsamplesextracted fromthesterilemediareservoirs.Theequipmentformeasuringinfluent andeffluentdissolvedoxygenwerekeptseparateforthedurationofthe experimentinordertopreventcontamination.Dissolvedoxygenprobes werecleanedusingaTergazyme(Alconox.Inc,WhitePlainsNY,USA) proteinremovalsolutionaftereverysetofmeasurements.
2.6. Computedx-raymicrotomographyimaging
X-rayCMTimagingwasconductedattheAdvancedPhotonSource (APS)facilityatArgonneNationalLaboratoryusingbeamline13BMDat GSECARS(GeoSoilEnviroConsortiumforAdvancedRadiationSources). Immediatelypriortoimaging,samplecolumnsweredisconnectedfrom influentandeffluentlines,andinjectedwiththecontrastagentsolution. Thecontrastagentconsistedofamedicalgradebariumsulfate(BaSO4) suspension(Micropaque,Guerbet)mixedwithsterilegrowthmedia.The 1.0g/mLstocksuspensionwasdiluteddowntoausableconcentration of0.33g/mL.Thecontrastagentwasinjectedintothesamplecolumns usingasyringe pumpat arateof1.2mL/hforthe𝑅𝑒=0.1 and1.0
columns,and5mL/hforthe𝑅𝑒=10columns.Atotalof2mLofcontrast agentsolutionwasinjectedintoeachcolumn.
Theaverageporevolume priortocolumninoculationis approxi-mately0.5mL,soapproximately4porevolumesofcontrastagentwas addedtoeachcolumn.Thedilutedsolution(0.33g/mL)wasselected tobalancetheabsorptionofX-raythroughthecolumnswiththe satu-rationlimitoftheX-raydetector(CCDcamera).Interestedreadersare referredtoIltis(2013)forathoroughdiscussionofbariumsulfate con-centrationrangesforsynchrotron-basedX-rayCMTofbiofilms,whereit wasreportedthattheusefulrangeofbariumconcentrationforcolumns 5–7mmindiameteris33%(0.33g/mL)to50%(0.5g/mL)barium sul-fate.
TheK-shellabsorptionedgeforbariumis37.4keVsoeachcolumn sectionwasscannedattwoenergies,oneabove(37.54keV)andone be-low(37.34keV)thisedge.Theentirelengthofeachcolumnwasscanned bymovingthesamplestageverticallyandgeneratingaseriesof over-lappingscansections. Volumetricreconstructionof eachsection was obtainedfromaseriesoftwo-dimensionalscansthatareobtainedviaa 180° rotationofthesamplestageover720incrementsateachheight. Thechoiceof720anglesisbasedonexperiencewiththe instrumenta-tionatthisparticularbeam-line.Thetheoreticalnumberofprojection anglesrequiredisthenumberofpixelstheareaofinterestcovers(as thesamplerotates360°)multipliedby1.5(or540angles).By oversam-plingwith720angles,blurisreducedandtheresultingimagesareofa higherquality;thisallowsmoreaccuratesegmentationandsubsequent quantitativeanalyses.
2.7. Imageprocessingandquantitativeanalysis
Thereconstructeddatasetshavedimensionsof695 × 695 × 470 voxels,avoxelresolutionof10.5µmandarestoredwith16-bit pre-cision. As a first preprocessing step a cylindrical region of interest
Fig.2. SmallsubsetofsegmentedCTimageoccupiedbybeads,biofilmand BaSO4 solution(a);theconnectivityindexisbasedonthetopologyofthebiofilm network.Porediametersobtainedwiththemaximuminscribedspheremethod (b);theporesizeindex(PSI)isbasedontheaverageporediameteroccupied bythebiofilm(green).Soliddistancesintheporespace(c);thesoliddistance index(SDI)isbasedontheaveragesoliddistancewithinthebiofilm(green). (Forinterpretationofthereferencestocolourinthisfigurelegend,thereader isreferredtothewebversionofthisarticle.)
(ROI)insidethecorewasextracted.Atotalvariationfilterwasapplied fordenoisingandanunsharpmaskfilterusedforedgeenhancement (Schlüteretal.,2014).Imagesegmentationofthegrayscaledatafocused onisolatingthreephases:thebiofilm,theBaSO4suspension (represent-ingtheaqueousphase)andthesolidphase(glassbeads).Forthesedata, propersegmentationrequiredthedevelopmentofanovelsegmentation algorithmthatincorporatedcomplementaryinformationfromvarious imagesources.DirectisolationoftheBaSO4 wasfacilitatedusingthe increasedabsorptionintheabove-Ba-edgevs.below-Ba-edgedatasets, whichisreflectedbyhighintensityinadifferenceimage.However,the BaSO4suspensionhadsmall-scaleheterogeneityduetolocallyvarying bariumconcentrations,likelyasideeffectofusingabarium concentra-tiononthelowendoftheapplicableconcentrationrangeof33–50%. SegmentationoftheBaSO4 suspensioneveninlow concentration re-gionscanthereforebeimprovedfurtherbydirectlyevaluatingthe de-greeofsmall-scaleheterogeneityin agradientimage.Thebeadsand thebiofilmexhibitedhomogeneousandindependentlydistinguishable X-rayabsorptionatboththeaboveandbelowedgescanningenergies. Sinceoneimagesuffices,isolationofthebeadsandbiofilmwas accom-plishedusingthebelow-edgeimagedatasets.
AMarkov random field(MRF) segmentationalgorithm(Kulkarni etal.,2012;Schlüteretal.,2014)wasextendedtoallowformultiple classstatisticsfromvariousimagesources.Atthecoreofthismethod,a combinatorialoptimizationproblemissolvedinordertofindalabeling
̂ 𝐶thatsatisfies ̂ 𝐶=𝑎𝑟𝑔𝑚𝑖𝑛 [ 𝐼 ∑ 𝑖=1 𝑁 ∑ 𝑗=1 𝛼𝑖 ( ln √ 2𝜋𝜎2 𝑐,𝑖+ (𝑔𝑖(𝐱 𝑗)−𝜇𝑐,𝑖)2 2𝜎2 𝑐,𝑖 ) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ class statistics + ∑ {𝐱𝑗,𝐲𝑗}∈Π 𝛾(𝑐(𝐱 𝑗),𝑐(𝐲 𝑗)) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ class boundaries (3) with 𝛾(𝑐(𝐱 𝑗),𝑐(𝐲 𝑗))= { −1, 𝑐(𝐱 𝑗)=𝑐(𝐲 𝑗) +1, 𝑐(𝐱 𝑗)≠ 𝑐(𝐲 𝑗) (4) Here,Iisthetotalnumberofevaluatedimages(below-edgeimage, gra-dientimageanddifferenceimage),Nisthetotalnumberofvoxels evalu-ated(withcoordinatex j),Πisthepopulationofallpairsofneighboring voxelsatcoordinatesx andy ,c(x j)istheclasslabelatx j(beads,biofilm
orBaSO4suspension),𝜇c,i and𝜎2𝑐,𝑖 areclassmeanandvariancein a
specificimagei,gi(x j)isthegrayvalueatthecoordinate x j inimage iand𝛼i isauser-defined,image-specificweightingfactorthat deter-minesthecontributionofeachlikelihoodtermforagivenclassrelative tothepenaltytermforclassboundaries.Inotherwords,aclasslabelat acertainlocationisverylikely,if(i)thelocalgrayvaluesinallimages isclosetothespecificclassmeanfortheseimagesandif(ii)the ma-jorityofneighborsalreadybelongtothesameclass.Classupdatingwas achievedinadeterministicorderdenotedasiterativeconditionalmodes (ICM),i.e.startingatonecorneroftheimagethelabelforeachvoxel wasreplacedbytheclassthatminimizesthecontributiontoEq.(3). Thealgorithmwasstoppedafterthreeloops.Valuesfor 𝜇c,i and𝜎𝑐,𝑖2
havetobedeterminedpriortosegmentation,whichwasdoneby evalu-atingthejointprobabilities,asexplainedintheAppendix.Classification errorsintheMRFsegmentationresults,duetopartialvolumeeffects, wereremovedviapost-processing,whichisalsoexplainedinthe Ap-pendix.Theentireworkflowfrompreprocessingtoimagesegmentation andpost-processingisbasedontheQuantImimageprocessinglibrary (Schlüteretal.,2014;Vogeletal.,2010).
The vertical series of eight segmented volumes is subsequently mergedintoone columnvialandmarkregistrationinAvizoFire8.3. Thatis,twoconsecutivevolumesoverlappingby25%andpairsof iden-ticalcoordinateswithintheseoverlapregionshavetobeidentifiedby trackingeasilyidentifiablefeatures.Fig.1(e)depictsthemergedcolumn forasamplegrownunderhighflowrateconditions(450mL/h,𝑅𝑒=10) aftersegmentation.
Thecolumnsareanalyzedforeachverticalsectionindividuallyin ordertodetectchangeswithrespecttoinletdistance.Theinvestigated propertiescomprisestandardpropertieslikeporosity,biofilmvolume, biofilmsurfacearea,biofilmthicknessandvolumepercentageattached tosidewalls.Inaddition,thespatialpatternsofgrowthandattachment arecharacterizedwiththreenormalizedindexesthatcoverdifferent as-pectsofbiofilmconfigurations,asdemonstratedforasmallsubsetin Fig.2.
Theconnectivityindex(CI)characterizeswhetherthebiofilmiswell orpoorlyconnectedbymeansoftheEulercharacteristic𝜒.This topo-logicalmeasureisdefinedas(Vogeletal.,2010)
𝜒 =−+ (5)
where isthenumberofisolatedobjectsofthematerialofinterest, isthenumberofredundantconnectionswithinallmaterialclusters andisthenumberofcavities(e.g.isolatedbackgroundclusters com-pletelyenclosedbythematerial).TheEulercharacteristicoftheentire porespaceinabeadpack(𝜒ps)isusuallynegative,becauseitiswell con-nectedwithahighnumberofredundantloopsaroundthebeads().A normalizedconnectivityindexforthebiofilmcanbecomputedasfrom theEulercharacteristicofthebiofilm(𝜒bf)(Herringetal.,2015)as
𝐶𝐼= 𝜒𝑏𝑓 𝜒𝑝𝑠
(6) Here,CI<1indicatesanimpairmentinbiofilmconnectivityduetothe presenceofflowchannelsofbariumsulfatesolution,whereasCI>1 im-pliesthatthecoexistenceofbiofilmandBaSO4solutionwithinthepore
spaceevenincreasesthenumberofredundantloopswithinthebiofilm network.
Theporesizeindex(PSI)isbasedontheanalysisofporediameters bythemaximuminscribedspheremethod(Fig.2(b)). ThePSIisthe ratiooftheaverageporediameteroccupiedbybiofilm(dbf)dividedby theaverageporediameteroftheentireporespace(dps)
𝑃𝑆𝐼=𝑑𝑏𝑓 𝑑𝑝𝑠
(7) Forthismetric,PSI<1indicatespreferenceofbiofilmtooccupypore constrictionsandavoidlargerporebodies.
Thesoliddistanceindex(SDI)isbasedontheanalysisofEuclidean distancesfromanylocationintheporespacetotheclosestsolidphase voxel(Fig.2(c)).The SDIis constructed bynormalizingtheaverage distancewithintheregionoccupiedbythebiofilm(ebf)bytheaverage distanceoftheentireporespace(eps)
𝑆𝐷𝐼= 𝑒𝑏𝑓 𝑒𝑝𝑠
(8) Forthismetric,SDI<1indicatespreferenceofbiofilmtoattachtosolid surfacesandavoidporecenters.Allquantitativeanalyseswerecarried outwithAvizoFire8.3andQuantIm.
2.8. Hydraulicconductivity
Transducer-based hydraulic conductivities were calculated using Darcy’slawwrittenforunidirectionalaxialflow(Bear,2013)
𝑣𝑧=− 𝜅𝑧𝑧 𝜇 ( 𝜕𝑝 𝜕𝑧−𝜌𝑔 ) (9) wherevzisthesuperficialvelocity(m/s),𝜅zztheaxialcomponentofthe permeabilitytensor(m2),gthegravitationalconstant(m/s2),and𝜕p/𝜕z thepressuregradient(Pa/m).Eq.(9)canbewritteninthefollowing simplifiedformfortheexperimentalsystem
𝑄 𝐴=−𝐾
ΔΦ
𝐿 (10)
HereΔΦisthenethydraulicheadchangeacrossthecolumn(m),Lthe totallengthofthecolumn(m),andKthehydraulicconductivity(m/s) thatisrelatedtopermeabilityby𝐾=𝜅𝑧𝑧𝜌𝑔∕𝜇.Notethatthehydraulic
headisdefinedbyHubbert’spotentialΦ(𝑧)=𝑧+𝑝(𝑧)∕(𝜌𝑔),sothatΔΦ simplyrepresentsthechangeinthehydraulicheadbetweentheinlet andtheoutletofthecolumns,ΔΦ =Φ𝑜𝑢𝑡𝑙𝑒𝑡−Φ𝑖𝑛𝑙𝑒𝑡.
Transducer-basedhydraulicconductivitiesforsampleporousmedia areusuallyestimatedbyscanningarangeofflowratesandproducinga linearfittothecorrespondingpressuredrops.Here,inordertoreduce uncertaintiesintroducedbytransducernoiseinthefit,awiderangeof flowrates(0–2500mL/h)wereapplied.Thisintervalextendsslightly beyondwhereEq.(10)isvalidintoatransitionalregimewherepressure dropandflowratearenonlinearlycorrelated(Bear,2013).To accom-modateforthisnon-linearity,theDarcy–Forchheimerequationwitha quadratic-in-velocitycorrectionwasusedinsteadincalculatingthe pre-growthconductivities.
Post-biofilm-growthhydraulicconductivitiesanduncertaintieswere calculatedusingEq.(10).Apotentialcauseofuncertaintyinthe mea-surementwasbiofilmgrowingintheinlettubing(despitesignificant ef-fortstopreventsuchgrowth),thisleadingtoadecreaseofpressuredrop, ΔPtubing,whentheinlettubingwaschanged(Section2.3).Wetherefore calculatedalowerboundofthepermeabilityusingthevaluesof pres-suredropaveragedoverthelast10hofeachexperiment,andanupper boundbysubtractingthecorrespondingΔPtubingfromtheaverage pres-suredrop.
Image-basedhydraulicconductivitieswerecalculatedusingthe fol-lowing Kozeny–Carman relationship (Bear, 2013) to compare it to transducer-basedestimates 𝐾=𝜌𝑔 𝜇 1 𝛽𝜏2 1 2 [ 𝜑3 (1−𝜑)2 ] (11) Inthisexpression,theparametersaredefinedaspreviously;inaddition, isthespecificsurfacearea(theinterfacialsurfaceareatovolumeratio ofthesolidphase),𝜏 isthetortuosityofthemedium,and𝛽 isaconstant. Forsimplegranularmediatheprefactor1/𝛽𝜏2isusuallyassumedtobe equalto1/5(Bear,2013).Wecalculatedthepre-growthdirectlyfrom the3Dimagesusingvaluesobtainedfortheglassbeadphaseinthedry scans.Thepost-growthvalueof wascalculatedbyconsideringthe biofilmandglassbeadsasthesolidphase.Thesumoftheinterfacial areasofbiofilmandglass beadsthatwereexposedtotheporespace wasusedforthispurpose.
OnewaytocalculateKusingEq.(11)istocomputetheglobal val-uesfor𝜑andaswidth-weightedaveragesofallthesections.However, averagingtendstoeliminatequitealotofpore-scaleinformation espe-ciallywhenthebiofilmphaseisnon-uniformlydistributedaxially. In-stead,Eq.(11)wasusedtocomputethehydraulicconductivityofeach columnsectionindependentlyand,inanalogywiththermalor electri-calresistance,theequivalent(effective)hydraulicconductivity(Keq)ofa columnwascalculatedastheharmonicmeanoftheconstituentsections (Bear,2013) 𝐿 𝐾𝑒𝑞 = 𝑁 ∑ 𝑖=1 𝐿𝑖 𝐾𝑖 (12)
whereListhetotallengthoftheevaluatedregion(cm),Liisthelength ofsectioni(cm),Nisthetotalnumberof sections,andKi isthe
hy-draulicconductivityof sectioni. Treatingeachimagedsectionasan independentlayer(Li)allowsforamorerealisticwayofaccountingfor non-uniformspatialdistributionofbiofilmsandtheireffectonK.
3. Results
3.1. Porousmediacharacterization
Bulkcharacterizationoftheporousmediapriortoflowexperiments providesasimplefirstcheckontheself-consistencyofimagingandthe post-processingworkflow.Tocomparewithgravimetricresults,global image-basedporositywascalculatedasaweightedaverageofthevalues fordifferentcolumnsections.Thebulkandimage-basedinitialcolumn porositieswere0.4000 ± 0.0075and0.4000 ± 0.0089,respectively. Thisexcellentmatchisrathersurprisingandastrongargumentforthe adequacyandrobustnessofthedevelopedimageprocessingworkflow. Thepre-growthbulkandimage-basedhydraulicconductivities(K)were 0.0181 ±0(cm/s)and0.0207 ± 0.0019(cm/s),respectively, demon-stratingverygoodagreementbetweenthetwomethods.Thesevalues areconsistentwiththegeneralrangeofvaluesreportedforsimple gran-ularmedia(Bear,2013).Theaveragesurface-area-to-volumeratioofthe media,,priortogrowthwascalculatedtobe4.22(1/mm).
3.2. Oxygenutilization
Themeasuredeffluentdissolvedoxygenconcentrationsnormalized bytheinfluentconcentrationarereproducedinFig.3.InfluentDO con-centrationsremainedstablearoundthesaturationlimitforoxygenin thegrowthmediaforthedurationoftheexperiment(theestimated sat-urationlimitwas8.05 ±0.29mg/L,whichwasusedtonormalizethe valuesinFig.3).Oxygendistributionshowedamarkedsensitivityto flowrate.Thecolumnssubjectedtothelowestflowratemaintained al-mostnegligibleeffluentoxygenconcentrations.Theintermediateflow rateproducedasimilarcurvebutshowedlate-timerecoveryforatleast oneof thecolumns. Insharpcontrast,thehighestflowratecolumns producedamoredynamicresponseandmaintainedanaverageeffluent concentrationaroundhalfthemagnitudeoftheinfluentconcentration throughoutthegrowthphase(fluctuationsareboundby∼1.5–6mg/L).
Fig.3. Temporalrecordoftheeffluentdissolvedoxygenconcentration (normal-izedbytheinfluentconcentration)forthe6experimentalcolumns.Each col-umninthefigurerepresentsmeasurementsmadeatthecorrespondingReynold’s numberattheonsetoftheexperiment.
3.3. Structuralevolutionoftheporespace
Inordertocharacterizethenatureofbiofilmgrowthatdifferentflow rates,theaxialdistributionsofanumberofstructuralmeasureswere studied.Spatialprofilesforthesemeasuresalongtheflowdirectionare plottedinFig.4.Thechangeinporosityinacolumn(beforeandafter growth)isthemostobviousmetrictoindicatetheamountof bioclog-ging.Fig.4(a)showsthattheintermediateflowrate(𝑅𝑒=1.0)resulted inthelargestreductioninporosity,followedbythehighest(𝑅𝑒=10), andlowestflowrates(𝑅𝑒=0.1),respectively.TheprofilesinFig.4 fur-thershowthattheextentofporosityreductionvariedalongtheaxial direction(z)inallsixtestcases,butlessextensivelysoatthelowest flowrate.
Thethree-dimensionalvisualizationsshown inFig.4arein clear agreementwiththesefindingsasasignificantlylesseramountofbiofilm isobservedinthe𝑅𝑒=0.1columns,andadenserandgreatervolume ofbiofilmisobservedinthe𝑅𝑒=1.0columns.Itisalsoworthnoting thatweareabletodistinguishthedirectionofflow(upwards)fromthe images,andobservelessrigorouslyattachedfeaturessuchasstreamers (Drescheretal.,2013),despitetheconcernmentionedinthe introduc-tionthattheBaSO4 methodmayscour ordetachsuch moreweakly attachedbiofilmcomponentswhenthecontrastagentisaddedtothe columns.Wefurtherexaminedthebiofilm-solid,andbiofilm-fluid in-terfacialareasperunitvolume.Figs.4(b)and(c)showthatthese mea-suresarefairlysimilarforthe𝑅𝑒=1.0and𝑅𝑒=10columns,butslightly largerfor𝑅𝑒=0.1columns.
Inordertoassessbiofilmformationinplanestransversetotheflow direction,wecalculatedthepercentageofthetotalattachmentsurface areawhichisassociatedwiththebiofilmthatisfixedonthesidewalls ofeachcolumnsectionasopposedtobeingattachedtothesurfaceof glassbeadswithinthesamesection.Thismeasureprovidessome indica-tionofthelateraldistributionofbiofilmandthedegreeofpenetration ofbiofilmintotheglassbeadmatrix.Theresultsindicatethata signif-icantlylargerfractionofbiofilmwasattachedtothecolumnsidewalls atthehighestflowrate(>35%inthefirst10mmofthetestsection) comparedwiththeintermediateflowratecolumns(∼27%inthefirst 10mmofcolumnelevation)(Fig.6(a)).Thisdifferencewasobserved fortotalaveragebiofilmvolumesof0.061cm3and0.085cm3forthe highestandintermediateflowratesrespectivelyinthefirst10mmof thecolumns.Percentsidewallattachmentforthelowestflowratewas relativelyinvariantintheaxialdirection.Incontrast,thevaluesforthe intermediateandhighestflowratesshowaconsistentdecrease(∼10%) towardtheoutlet.
Thethreestructureindiceshighlightdifferentaspectsofchanging biofilmconfigurationswithchanging flowrates.There wasa consis-tenttrendtowardshigherconnectivityindices(CI)withincreasingRe (Fig.6(b)). At 𝑅𝑒=0.1 biofilm connectivity was lowest (CI≤1) be-causethevolumefractionofbiofilmwasalsolowest,biomassbeing dis-tributedinsmaller,isolatedpatches.Atintermediateflowrates(𝑅𝑒=1) thebiofilm hadamuch higherconnectivity(1<CI<3),becausethe biofilmoccupiedtheporespacealmostcompletely(lowestporosityin Fig.4(b)).Therewasagradualreductioninconnectivitywithinlet dis-tance,becausethebiofilmgetsmorecompact.Thatis,sinceflowpaths occupiedbyBaSO4solutiondecreasedwithinletdistance,therewere lessredundant loopsinthebiofilm aroundthese flowpaths.This CI reductionwithinletdistanceisinlinewithdecreasingporosityand de-creasingreactivesurfacearea(Fig.4(b)and(c)).The𝑅𝑒=10columns exhibitedtheoppositetrendofincreasingconnectivitystartingatsmall isolatedpatchesdirectlyattheinlet(CI≈1)andendingwiththe high-estconnectivityofallcolumnsintheupperpart(CI>3)becausebiofilm andflowchannelsofBaSO4forcomplexintermingledstructuresalso ex-hibitedthehighestreactivesurfacearea(Fig.4(c)).
Thedifferences inthesoliddistanceindiceswerelesspronounced (Fig.6(c)).Ingeneral,SDI≤1becausebiofilmgrowthwasalways initi-atedonsolidsurfacessothatbiofilmhadatendencytobelocatedclose tosolidinterfaces.TheSDIwashighestatintermediateflowrates be-causethebiofilmoccupiedthelargestpartoftheporespacesothatthe averagedistanceofthebiofilmebf approachedthatoftheporespace
eps.Boththehighest(𝑅𝑒=10)andlowest(𝑅𝑒=0.1)flowrate exhib-itedagradualincreaseinSDIfromtheinlettowardstheoutlet.Inboth casesbiofilmclustersdirectlyattheinletweresmallanddirectly at-tachedtograinsurfaces.Withincreasinginletdistancethevolume
frac-Fig.4.Spatialdistributionofporositychange(a),biofilm-fluidsurfaceareapervolume(b),andbiofilm-solidsurfaceareapervolume(c).Datapointsrepresentthe averagesoftwoexperimentsatindividualsections.Errorbarsrepresentonestandarddeviation.
tionandsurfaceareaalsoincreasedandsodidthegrowthintopore centers(Fig.4(b)and(c)).Directlyattheoutlettherewasaconsistent increaseinSDIamongallcolumnsthatmightbecausedby accumula-tionofbiomass.Theporesizeindex(PSI)exhibitedverysimilar behav-iorandthereforecarriedredundantinformationatleastforthe investi-gatedglassbeadmedium(Fig.6(d)).Therewasatendencyofthebiofilm tooccupysmallerporeconstrictionsforallflowrates,whichwasless pronouncedatintermediateflowrates(𝑅𝑒=1)becauseatthesehigh volumefractionstheaverageporediametercoveredbythebiofilm(dbf) approachedthatoftheentireporespace(dps).Atthehighestflowrate
(𝑅𝑒=10)therewasagainagradualincreaseinPSIwithinletdistance, becauseintheupperpartofthecolumnbiofilmgrowthoraccumulation extendedmoretowardsbiggerporebodies.
3.4. Bioclogging
Fig.7showsthecomparisonbetweentransducer-basedand image-basedhydraulicconductivitiesbeforeandafterbacterialgrowth.The shaded areas in the figure represent the uncertainty bounds of the transducer-basedmeasurements due topotential growthin the inlet tubing,computedasdescribedinSection2.8.Thetransducer-measured changeinhydraulicconductivityvariedbetween1to2ordersof mag-nitudefor all columns, values that are comparabletothe range re-portedin otherinvestigations (e.g.Cunningham etal., 1991;Seifert
andEngesgaard,2007;Thullner,2010).Thelargestmeandecreasein
Kwasobserved forthe𝑅𝑒=1.0 columnswhilethelowest flowrate columns(𝑅𝑒=0.1)producedthesmallestmeandecreaseinhydraulic conductivity.Fig.7(a)showsthattheKozeny–Carmanrelationshipwith 1∕𝛽𝜏2=1∕5(modelA)predictedthetrendofreductioninKatthe dif-ferentflowrate,buttendedtosystematicallyunderestimatethe magni-tudescomparedwithtransducer-basedmeasurements,despitethe pref-actorbeingrepresentativeattheonsetoftheexperiments.
Apotentialcauseoftheobserveddeviationbetweenthetwo meth-odsisanincreaseinthetortuosityofthemediaafterbacterialgrowth. Wecalculatedthepre-andpost-growthtortuositiesdirectlyfromthe imagesusingtheCentroidPathTortuosity modulein AvizoFire8.3. Thismodulecomputesthetortuosityofapathformedbythecentroids oneachplanealongthez-axisofabinary3Dimage.Thebiofilmand solidphaseswerecombinedintheimageandthentheimagewas bina-rizedbeforethetortuositywascalculatedforeachstackofimages.An averageofthetwocolumnsforeachflowrateispresentedinFig.7(b) (valuesarenormalizedbypre-growthtortuositiescomputedusingthe samemethod).Thecomputedvalueswerethenusedtocorrectthe pref-actorin theKozeny–Carmanrelationship (modelB). Fig.7(c)shows thataccountingforanincreaseintortuositysignificantlyimprovedthe comparisonbetweentransducer-basedandimage-basedcomputations ofpost-growthhydraulicconductivityforallflowrates.Theobserved increaseintortuosityisslightlylargerthantherangeofvaluesobtained viasimulationsof2Drandommediafor𝜑<0.3(Hymanetal.,2012; Matykaetal.,2008).
4. Discussion
A combination of results from different measurements supports thehypothesis thatgrowthunder𝑅𝑒=0.1wassignificantly nutrient-limited. The almost complete depletion of dissolved oxygen at this flowrate(Fig.3)supportsthispicture,althoughbiofilmgrowinginthe inlettubing couldhavecontributed totheconsumptionof inletDO, andtherebyhavecontributedtotherecordedpressuredrops.Limited growthat𝑅𝑒=0.1isalsoreflectedinthemarkedlylowerreductionin porosity(Figs.4(d),and5(a))andhydraulicconductivitywhen com-paredwithhigherflowrates.Theaveragebiofilmvolumeatthisflow rateisrelativelyuniformaxiallywithlowconnectivityamongdispersely distributed biofilm clusters that are preferentially attached tograin boundariesandporeconstrictions.Sensitivityofbiofilmstructuretothe
Fig.5. Visualizationsofbiofilmdistributionincolumnssubjectto𝑅𝑒=0.1(a), 𝑅𝑒=1.0(b),and𝑅𝑒=10(c).Glassbeadsaregray,andbiofilmispurpleinthe onlineversion.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)
Fig.6. Spatialdistributionsofthecontributionofsidewallattachmenttothe totalbiofilmattachmentsurfacearea(a),thenormalizedconnectivityindex(b), thesoliddistanceindex(c),andtheporesizeindex(d).
Fig.7.(a):Transducer-basedandimage-basedestimatesforreductioninhydraulicconductivityatdifferentflowrates.Image-basedresultsarecalculatedusing Eq.(11)with1∕𝛽𝜏2=1∕5(modelA),andtortuosityvaluesdirectlycomputedfromimages(modelB).Theshadedareashowsthepotentialuncertaintyin
transducer-basedmeasurementsduetogrowthininlettubings.(b):Ratiosofpre-andpost-growthtortuositiesobtainedviadirectanalysisofimages. availabilityofoxygenhasbeenreportedpreviously(e.g.Changetal.,
2015).
Incontrast,biofilmgrowthisimprovedattheintermediateand high-estflowrates(compareFig.5(a)–(c)).Weobservedagradientinaverage biofilmvolumethatincreasedtowardthetopofthecolumnsat𝑅𝑒=1.0 and10,alikelyindicationofshear-inducedsloughingofcellsand sub-sequentaccumulationneartheoutlet(an1/8-inchnarrowopeningthat connectstheporoussectiontoexternaltubing).Interestinglyother gra-dientsinbiofilmconfigurationsshowedoppositetrendsfor𝑅𝑒=0.1and 𝑅𝑒=10.Atintermediateflowratesthebiofilmgrowthwasmoreevenly distributedwithintheporespaceintermsofoccupiedporesizesand graindistances.Thereactivesurfaceareaandconnectivitydecreased slightlytowardstheoutlet.Atthehighestflowrate,inturn,therewasa distinctshifttowardsgrowthinporeconstrictionsandalonggrain sur-facesespeciallyclosetotheinletaswellasadistinctincreaseinbiofilm volume,reactivesurfaceandconnectivitywithinletdistance.Amore subtleformofheterogeneityisevidentintheaveragepercentsidewall attachment,whichdecreasedsignificantlybeyondthefirstfewsections for𝑅𝑒=1.0and10,andisinvariantfor𝑅𝑒=0.1.Thesetrendssuggest that,especiallyunderthehighershearflows,biofilmgrowthundergoes atransitionwhereregions nearthesidewallareincreasinglyless oc-cupiedbybiofilmtoward theoutlet. Thisis becausepores alongthe sidewallsarewiderthanporesbetweenglassbeadsduetosub-optimal packingandtheythereforeimposealowerresistancetoflow.
Theinhomogeneitiesin thespatialdistributionofbiofilmsappear tobelinkedtoregionswheredramaticchangesinflowtakeplace.The threeexamplesobservedhereare(i)increasedtendencyofbiofilmsto forminthesidewallregionsneartheinlet.Thistendencycouldbe a consequenceofthegenerallyhigherconcentrationsofdissolvedoxygen neartheinlet,andtheflowfieldstillbeingaffectedbythe converging-divergingnozzle-likestructureof thecolumninlet; (ii)accumulation ofbiofilmneartheoutletwhereflowisconvergingintoamore con-strictedopeningasdiscussedabove;and(iii)atthehighestflowrate thetendencyofbiofilmtooccupyporeconstrictionsandgrainsurfaces directlyclosetheinlet,aneffectthatdisappearsagainatgreaterinlet distances.Thisindicatesthathighershearflowsinthemainflowpaths neartheinlethindersthebiofilmfromoccupyingthecenterofbigger porebodiesinthevicinityoftheinlet.
Thefactthatcorrectingfortortuositysignificantlyimprovesthe com-parisonbetweentransducer-andimage-basedpost-growth permeabili-tiessupportsthenotionthatbiofilmgrowthcancompletelytransform thestructureofpore-scaleflow(Drescheretal.,2013).Theimage-based measurementsfor𝑅𝑒=0.1and𝑅𝑒=10canpotentiallybefurther im-provedbyusingotherporespaceattributesthantheharmonicmean ofporosities.Onewayforwardwouldbetocomputecriticalpath con-ductivities(Friedman andSeaton,1996),bysearching forthelowest conductivity alongthe pathof lowestflow resistance, which in our studywould likely be situated close tothe outletwere biofilmwas
accumulating.Although thevolume fraction andassociated porosity of this type of localgrowth is small, itcan imposea dominant im-pacton effectivepermeability.Similarresults havebeenreportedby Bielefeldtetal.(2002)wheredecreasesinhydraulicconductivityofup to3ordersofmagnitudewereobserveddespiteamere3–8percent de-creaseinporosityduetobiofilmgrowth.
Weshouldnotethatthetransducer-derivedpost-growth permeabili-tiescarrysomeuncertaintyaswell,becauseobservedfluctuationsmake itdifficulttoobtainanaccuratevalueforpressuredropimmediately beforetheterminationoftheexperiment.Implementinganaveraging windowadjacenttotheendoftheexperimentcanstabilizethereading, butintroducesinformationfromearliertimesthatmightnot necessar-ilyrepresentthesnapshotstudiedafterimaging.Consideringthisand thesimplicityoftheKozeny–Carmanmodel,image-basedcalculations demonstrateverygoodaccuracy.Onceactualtortuositieswereusedto predictthereductioninhydraulicconductivity,thetrendwithRewas verywell-matched(modelBinFig.7).
Basedontheoverallpatternofreductioninhydraulicconductivity atdifferentflowrates,wehypothesizethatthebiocloggingwas influ-encedbyatrade-off betweentheavailabilityofnutrients(mainly dis-solvedoxygen)andshear-inducedsloughing.Biofilmsgrownunderan initialReof1.0resultedinaslightlylargeraveragereductionin hy-draulicconductivityandporosity.Bothparametersdecreasedasflow rateincreasedinthecurrentroundofexperiments.Ourinterpretation ofthistrendisthat,asflowrateincreased,athresholdwascrossedat whichpointoxygenis nolongeralimitingfactorin biofilmgrowth, andcontinuousgrowthwaspromoteduntilshearstressinducedbythe increasinglyrestrictedflowinitiatessloughing.
5. Limitations and future work
Balancingcompletecoverageoftheporespacebythecontrastagent, whileminimizingsloughingof biomassistheprimarychallenge dur-ingimaging.Theimageprocessingworkflowimplementedhereenabled asignificantimprovementintheaccuracyofphasesegmentationover previouseffortsbyaccountingfortheheterogeneitiesinthespatial dis-tributionof thebariumsulfatecontrast agent. Developmentof more sophisticatedcontrastagentsandtailoredimageprocessingalgorithms couldfurtherimprovetheresolutionofthemethodandreduceits in-trusivity.Becausewe usemicroimaging asamodel-drivenpredictor, thesensitivityofimage-basedmeasurementsdependsonthe complex-ityof themodelsusedtodeducethem. Wewouldexpect thatusing modelsthat carry more informationon themorphology of thepore spacesignificantlyimprovetheaccuracyof themethod,perhaps be-yondwhatispossibleusingtransducermeasurements.Forinstanceone coulddirectlytakeintoaccountlocalvariationsinvelocityand pres-sureandtheireffectonpermeabilityinadirectnumericalsimulation ofthepost-growthflowfield(e.g.Peszynskaetal.,2015).Regardless,
computationsofpermeability/hydraulicconductivityusingtheKozeny– Carmanmodelandthemeasuredsurface-area-to-volumeratios, poros-ity,andtortuosity(allpurelyimage-basedmeasurements)demonstrated verypromisingfidelity.
Anothersteptowardbetterunderstandingthemorphology, distribu-tionandquantityofbiomassgrowingwithinporousstructuresisto sys-tematicallystudyabroaderrangeofflowrateandnutrientconditions, witheach conditionreplicatedseveraltimes.Inthisperspective, the presentresultsshowgreatpromiseforfutureuseofthemethodin under-standingthereportedheterogeneitiesinphysicalpropertiesofporous mediasubject tomicrobial growth(e.g.acousticsignatures,complex conductivity,etc.)andthepost-growth3Dstructureoftheporespace (AbdelAaletal.,2010;AtekwanaandSlater,2009;Davisetal.,2006; 2009;2010).Imagingofrelativelylargesampleswasachievedhere, en-ablingthestudyofbulkgrowthindicatorsinresponsetoaprescribed flowrate,aswellaslocalvariationsingrowthinthemodelsystems. Newstructuralindiceswereintroducedinthisstudythatcoververy dif-ferentaspectsofbiofilmconfigurations;thesenewindicesshouldhelp facilitatesystematicstudiesinthefuture.Thedegreetowhichthese re-sultsaregeneralizableinevitablydependsonthechoicesmadeduring thedesignoftheexperimentalsystem.Regardless,thisworkhashelped toestablisheffectiveprotocolssothatfutureworkcanfocusonmore complex porestructures andexploringabroaderrangeof replicated conditions.
6. Conclusions
3Dvisualizationofbiofilmstructurewasachievedforthreedistinct hydrodynamicconditionsinopaqueporousmedia.Microimagingwas usedtotrackthestructuralchangesoftheporespacesduetobiofilm growth,whichwerecross-referencedwithbulkmeasurementsof pres-suredropandoxygenutilization.Distinctgrowthandlocal morpho-logicalpatternswereobserved forgrowthin columnssubject to dif-ferentflowrates.Excellentagreementwasfoundbetween transducer-derived hydraulic conductivities andimage-based estimates using a simpleporosity-permeabilityrelationshippriortogrowth.Post-growth permeabilitiesprovedmorechallengingtopredictduepossiblytothe development of heterogeneities in poremorphology. Yet, very good agreementwasobservedbetweenthetrendsofhydraulicconductivity reductionatdifferentflowratesusingthetwomethods,andtheresults improvedwhentheincreased(actual)post-growthtortuosityofthepore spacewasaccountedfor.Biocloggingwasfoundtodependnon-trivially onflowrate,likelyafunctionofcompetingmasstransfer(dissolved oxy-gendelivery)andshearstress.Theuseofabariumsulfatesuspensionas acontrastagentwasfurtherfine-tunedbyimplementinganovelimage processingworkflowthataccountsforinhomogeneitiesinthe attenua-tionofthefluidphase.Theresultsdemonstratetheutilityof microimag-ingusingX-rayCTinstudiesoftransformationofporousmediasubject tobiofilmgrowth.
Acknowledgments
ThisworkwassupportedbytheEnvironmentalRemediationScience Program(DE-FG02-09ER64734)undertheDepartmentofEnergy, Of-ficeofBiologicalandEnvironmentalResearch(BER),grant ER64734-1032845-0014978.ThisresearchusedresourcesoftheAdvanced Pho-tonSource,aU.S.DepartmentofEnergy(DOE)OfficeofScienceUser FacilityoperatedfortheDOEOfficeofSciencebyArgonneNational
Lab-oratoryunderContractNo.DE-AC02-06CH11357.Weacknowledgethe
supportofGeoSoilEnviroCARS(Sector13),whichissupportedbythe NationalScienceFoundation-EarthSciences(EAR-1128799),andthe DepartmentofEnergy,Geosciences(DE-FG02-94ER14466).Wewould liketothankMarkRiversatGSECARSattheAPSforassistancewith CTimaging.SOandBWweresupportedinpartbytheNationalScience FoundationundergrantEAR1141488.SSisgratefultothe Alexander-von-Humboldt Foundation for granting a Feodor-Lynen scholarship.
Theimageprocessing libraryQuantImisaccessible freeofcharge at
http://www.quantim.ufz.de.
Appendix A
A1. Segmentationofbiofilmdata
ThechallengeinsegmentingbiofilmimagesisthattheBaSO4 parti-clesarenon-uniformlydistributedintheporespacethatisnotoccupied bythebiofilm(Fig.A.1(a)).Thisresultsinbroadrangeofintensitiesfor theBaSO4phase.Asaconsequence,itcannotbeidentifiedasathird modeinthecorrespondinghistogram(Fig.A.1(d)).Inturn,the differ-encebetweenabove-edgeandbelow-edgeintensity(Fig.A.1(b))islow forbiofilmandbeads,sinceinbothphasestheelectronadsorptiondoes notchangewithasmallchangeinbeamenergy.Yetthedifferenceis highfortheBaSO4phaseandvarieswithbariumconcentration.This re-sultsinasinglepeakforbeadsandbiofilmandalongtailingforBaSO4 inthecorrespondinghistogram(Fig.A.1(e)).Thejointfrequency dis-tributionofthebelow-edgeandthedifferenceintensities(Fig.A.1(g)) isalreadysufficienttoidentifybeadsasanisolatedclusterinthe fea-turespace,butthereisagradualtransitionfrombiofilmtoBaSO4due tothevariationinbariumconcentration.Thisvariation,however,can beassessedbythelocalimagegradient(Fig.A.1(b)),whichislowin thehomogeneousbeadsandbiofilmandhasabroadrangeof intensi-tiesintheBaSO4filledporespace.Thisleadstoajointpeakatzeroin thegradienthistogramforbiofilmandbeads(Fig.A.1(e))andalong tailforBaSO4andthetransitionvoxelsatphaseboundaries.Thejoint frequency distributionofthebelow-edgeandthegradientintensities (Fig.A.1(h))exhibitstwoclustersatlowgradientintensities,onefor beadsandoneforbiofilm,whichareconnectedbyanarchofpartial volumevoxelsattheboundariesbetweenthetwophases,andextensive scatteringforBaSO4.
Thetwojoint probabilities(Fig.A.1(g)and(h)) arenowused to estimatetheclassstatisticsinEq.(3)withthefollowingworkflow:
1. Unimodalthresholding(Rosin,2001;Schlüteretal.,2014)isapplied toseparatethepeak(biofilmandbeads)fromthetail(BaSO4and phaseboundaries)inthegradienthistogram.Notethatthisthreshold correspondstothehorizontallineinFig.A.1(h).AROIofvoxelsthat belongtothepeakclassiscreated.
2. Thehistogramofbelow-edgeintensitieswithinthisROIisevaluated byaminimumsearch(Schlüteretal.,2014;Tsai,1995)todetectthe thresholdbetweenbeadsandbiofilm.Thiscorrespondstoavertical lineinFig.A.1(h).
3. Abeadlabelisassignedtoallvoxelsthatfulfillboththreshold re-quirementsandwhosejointfrequencyexceedsauser-defined thresh-old,e.g.1× 10−3inFig.A.1(h).Biofilmvoxelsarelabeledinthesame way.
4. Noiseobjectsinthelabelimageareremovedwithasizeexclusion filterandtheremaininglabelsaredilatedwithasphericalstructure elementofradius𝑟=4.Thedilatedareasareconsideredasphase boundariesandtherestisassignedtoBaSO4.
5. Steps1–4arerepeatedwiththedifferenceimageinsteadofthe gra-dientimageasverticalaxisinthefeaturespace(Fig.A.1(g)). 6. Thefinallabelimage(Fig.A.2(d))isobtainedbymergingthe
la-belimagesfromsteps4and5together,i.e.labelsthatcoincidein bothimagesarekeptandvoxelswithdifferentlabelsaresetbackto unassigned.
7. Theclassstatistics(𝜇c,𝜆and𝜎𝑐,𝜆2 )inEq.(3)canthenbeestimated
fromlabel-specifichistogramsineachinputimage.
Notethat theautomatedthreshold detectionmethodsin the pre-sentedworkflowmayfail,whenthevolumefractionofbiofilmorBaSO4 becomestoolow.Inthatcasethatvalueshavetobeadapted manu-ally.Wearecurrentlyimprovingtheworkflowbysubstitutingthe itera-tivethresholddetectionforsinglesourceimageswithmulti-dimensional
Fig.A1. Simpleandjointfrequencydistributionsforvariousinputdata:(a)2Dsliceofabelow-edgeimagefromamediumflowrate(𝑅𝑒=1.0);(b)2Dsliceof differencebetweenabove-edgeandbelow-edgeimage;(c)2Dsliceofgradientofbelow-edgeimage;(d)histogramofbelow-edgeimage;(e)histogramofdifference image;(f)histogramofgradientimage;(g)jointfrequencydistributionsofbelow-edgeanddifferenceimageincludingthresholds;(h)jointfrequencydistributions ofbelow-edgeandgradientimageincludingthresholds.
clusteringtechniquesthatallowforirregularthresholdsurfacesinthe featurespace.
DuringMarkovrandomfield(MRF)segmentationeachvoxelis as-signedaclasslabelaccordingtothepenaltytermforphaseboundaries andthesumoflikelihoodtermsofeachclassinEq.(3)(Fig.A.2(a)– (c)).Due toreformulation thesmallestvaluefor thelikelihoodterm isconsideredoptimal.Thelikelihoodtermismultipliedwiththe user-definedweightingfactorforeachimagesource,whichissettoalow valueof 𝛼𝜆=0.1,𝜆 =1,2,3,toincreasethe penaltyon phase
bound-ariesandthusinvokesmoothboundaries.TheMRFsegmentationresults
(Fig.A.2(e))arenotoptimalyetduetopartialvolumeeffects.Thatis, voxelsalongthebeadboundariesarepartiallyfilledwithbiofilm,which leadstoafalseassignmenttoBaSO4.Postprocessinghastobeapplied toremovethisunwantedeffect.Todoso,acubickernelwith73 vox-elsloopsthroughtheimage,detectsboundariesasneighborhoodswith morethanonelabelandsetsthecentralvaluetounassigned. Subse-quentlythelabelsareiterativelydilatedbackintounassignedareasby asimplemajorityrule,i.e.themostrepresentativelabelinacubic73 kernelisassignedtothecentralvoxeluntilnounassignedvoxelisleft. TheresultafterpostprocessingisdepictedinFig.A.2(f).
Fig.A2. Segmentationandpostprocessingresults:likelihoodofeachclassforagivengrayvalueaccordingtotheclassstatisticsin(a)thebelow-edgeimage,(b) thegradientimage,(c)thedifferenceimage;(d)2Dsliceofmergedlabelimagethatservesasatemplatetoestimateclassstatistics;(e)MRFsegmentationresults; (f)finalsegmentationresultsafterpostprocessing.
Supplementary material
Supplementarymaterialassociatedwiththisarticlecanbefound,in theonlineversion,atdoi:10.1016/j.advwatres.2018.03.018.
References
Abdel Aal, G.Z. , Atekwana, E.A. , Atekwana, E.A. , 2010. Effect of bioclogging in porous media on complex conductivity signatures. J. Geophys. Res.: Biogeosci. 115 (G3) . Armstrong, R.T. , Wildenschild, D. , 2012. Investigating the pore-scale mechanisms of mi-
crobial enhanced oil recovery. J. Petrol. Sci.Eng. 94, 155–164 .
Atekwana, E.A. , Slater, L.D. , 2009. Biogeophysics: a new frontier in earth science research. Rev. Geophys. 47 (4) .
Baveye, P. , 2010. Comment on ‘comparison of bioclogging effects in saturated porous media within one-and two-dimensional flow systems’ by martin thullner. Ecol. Eng. 36 (6), 835–836 .
Baveye, P. , Vandevivere, P. , Hoyle, B.L. , DeLeo, P.C. , de Lozada, D.S. , 1998. Environmen- tal impact and mechanisms of the biological clogging of saturated soils and aquifer materials. Crit. Rev. Environ. Sci. Technol. 28 (2), 123–191 .
Baveye, P.C. , Darnault, C. , 2017. Microbial competition and evolution in natural porous environments: not that simple. Proc. Natl. Acad. Sci. 201700992 .
Bear, J. , 2013. Dynamics of Fluids in Porous Media. Courier Corporation .
Beyenal, H. , Donovan, C. , Lewandowski, Z. , Harkin, G. , 2004. Three-dimensional biofilm structure quantification. J. Microbiol. Methods 59 (3), 395–413 .
Bielefeldt, A.R. , McEachern, C. , Illangasekare, T. , 2002. Hydrodynamic changes in sand due to biogrowth on naphthalene and decane. J. Environ. Eng. 128 (1), 51–59 . Carrel, M. , Beltran, M.A. , Morales, V.L. , Derlon, N. , Morgenroth, E. , Kaufmann, R. ,
Holzner, M. , 2017. Biofilm imaging in porous media by laboratory x-ray tomography: combining a non-destructive contrast agent with propagation-based phase-contrast imaging tools. PloS one 12 (7), e0180374 .
Chang, Y.-W. , Fragkopoulos, A.A. , Marquez, S.M. , Kim, H.D. , Angelini, T.E. , Fernán- dez-Nieves, A. , 2015. Biofilm formation in geometries with different surface curvature and oxygen availability. New J. Phys. 17 (3), 033017 .
Coyte, K.Z. , Tabuteau, H. , Gaffney, E.A. , Foster, K.R. , Durham, W.M. , 2017. Reply to bav- eye and darnault: useful models are simple and extendable. Proc. Natl. Acad. Sci. 201702303 .
Cunningham, A.B. , Characklis, W.G. , Abedeen, F. , Crawford, D. , 1991. Influence of biofilm accumulation on porous media hydrodynamics. Environ. Sci. Technol. 25 (7), 1305–1311 .
Davis, C.A. , Atekwana, E. , Atekwana, E. , Slater, L.D. , Rossbach, S. , Mormile, M.R. , 2006. Microbial growth and biofilm formation in geologic media is detected with complex conductivity measurements. Geophys. Res. Lett. 33 (18) .
Davis, C.A. , Pyrak-Nolte, L.J. , Atekwana, E.A. , Werkema, D.D. , Haugen, M.E. , 2009. Mi- crobial-induced heterogeneity in the acoustic properties of porous media. Geophys. Res. Lett. 36 (21) .
Davis, C.A. , Pyrak-Nolte, L.J. , Atekwana, E.A. , Werkema, D.D. , Haugen, M.E. , 2010. Acous- tic and electrical property changes due to microbial growth and biofilm formation in porous media. J. Geophys. Res.: Biogeosci. 115 (G3) .
Davit, Y. , Byrne, H. , Osborne, J. , Pitt-Francis, J. , Gavaghan, D. , Quintard, M. , 2013. Hy- drodynamic dispersion within porous biofilms. Phys. Rev. E 87 (1), 012718 . Davit, Y. , Iltis, G. , Debenest, G. , Veran-Tissoires, S. , Wildenschild, D. , Gérino, M. , Quin-
tard, M. , 2011. Imaging biofilm in porous media using x-ray computed microtomog- raphy. J. Microsc. 242 (1), 15–25 .
Drescher, K. , Shen, Y. , Bassler, B.L. , Stone, H.A. , 2013. Biofilm streamers cause catas- trophic disruption of flow with consequences for environmental and medical systems. Proc. Natl. Acad. Sci. 110 (11), 4345–4350 .
Dreszer, C. , Wexler, A.D. , Drusová, S. , Overdijk, T. , Zwijnenburg, A. , Flemming, H.-C. , Kruithof, J.C. , Vrouwenvelder, J.S. , 2014. In-situ biofilm characterization in mem- brane systems using optical coherence tomography: formation, structure, detachment and impact of flux change. Water Res. 67, 243–254 .
Friedman, S.P. , Seaton, N.A. , 1996. On the transport properties of anisotropic networks of capillaries. Water Resour. Res. 32 (2), 339–347 .
Gunjal, P.R. , Ranade, V.V. , Chaudhari, R.V. , 2005. Computational study of a single-phase flow in packed beds of spheres. AlChE J. 51 (2), 365–378 .
Herring, A.L. , Andersson, L. , Schlüter, S. , Sheppard, A. , Wildenschild, D. , 2015. Efficiently engineering pore-scale processes: the role of force dominance and topology during nonwetting phase trapping in porous media. Adv. Water Resour. 79, 91–102 . Hyman, J.D. , Smolarkiewicz, P.K. , Winter, C.L. , 2012. Heterogeneities of flow in stochas-
tically generated porous media. Phys. Rev. E 86 (5), 056701 .
Iltis, G.C. , 2013. Visualization and Characterization of Biofilm Spatial Distribution in Porous Media Using X-ray Computed Microtomography .
Iltis, G.C. , Armstrong, R.T. , Jansik, D.P. , Wood, B.D. , Wildenschild, D. , 2011. Imaging biofilm architecture within porous media using synchrotron-based x-ray computed microtomography. Water Resour. Res. 47 (2) .
Ivankovic, T. , du Roscoat, S.R. , Geindreau, C. , Séchet, P. , Huang, Z. , Charier, P. , Mar- tins, J.M. , 2017. Laboratory x-ray microtomography as a tool for 3d visualization of biofilm in porous media made up of zeolite. In: Microbiology Society Annual Confer- ence 2017 .
Kim, D.-S. , Fogler, H.S. , 2000. Biomass evolution in porous media and its effects on per- meability under starvation conditions. Biotechnol. Bioeng. 69 (1), 47–56 .
Kulkarni, R. , Tuller, M. , Fink, W. , Wildenschild, D. , 2012. Three-dimensional multiphase segmentation of x-ray ct data of porous materials using a bayesian markov random field framework. Vadose Zone J. 11 (1) . 0–0
Leis, A.P. , Schlicher, S. , Franke, H. , Strathmann, M. , 2005. Optically transparent porous medium for nondestructive studies of microbial biofilm architecture and transport dynamics. Appl. Environ. Microbiol. 71 (8), 4801–4808 .
Li, Z. , Hassan, A.A. , Sahle-Demessie, E. , Sorial, G.A. , 2013. Transport of nanoparticles with dispersant through biofilm coated drinking water sand filters. Water Res. 47 (17), 6457–6466 .
Majors, P.D. , McLean, J.S. , Fredrickson, J.K. , Wind, R.A. , 2005. Nmr methods for in-situ biofilm metabolism studies: spatial and temporal resolved measurements. Water Sci. Technol. 52 (7), 7–12 .
Manz, B. , Volke, F. , Goll, D. , Horn, H. , 2003. Measuring local flow velocities and biofilm structure in biofilm systems with magnetic resonance imaging (mri). Biotechnol. Bio- eng. 84 (4), 424–432 .
Matyka, M. , Khalili, A. , Koza, Z. , 2008. Tortuosity-porosity relation in porous media flow. Phys. Rev. E 78 (2), 026306 .
Neu, T.R. , Lawrence, J.R. , 2015. Innovative techniques, sensors, and approaches for imag- ing biofilms at different scales. Trends Microbiol. 23 (4), 233–242 .
Peszynska, M. , Trykozko, A. , Iltis, G. , Schlueter, S. , Wildenschild, D. , 2015. Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscal- ing. Adv. Water Resour. .
Rittmann, B.E. , 1993. The significance of biofilms in porous media. Water Resour. Res. 29 (7), 2195–2202 .
Rodríguez, S.J. , Bishop, P.L. , 2007. Three-dimensional quantification of soil biofilms using image analysis. Environ. Eng. Sci. 24 (1), 96–103 .
du Roscoat, S.R. , Martins, J. , Séchet, P. , Vince, E. , Latil, P. , Geindreau, C. , 2014. Appli- cation of synchrotron x-ray microtomography for visualizing bacterial biofilms 3d microstructure in porous media. Biotechnol. Bioeng. 111 (6), 1265–1271 .
Rosin, P. , 2001. Unimodal thresholding. Pattern Recognit. 34 (11), 2083–2096 . Schlüter, S. , Sheppard, A. , Brown, K. , Wildenschild, D. , 2014. Image processing of multi-
phase images obtained via x-ray microtomography: a review. Water Resour. Res. 50 (4), 3615–3639 .
von der Schulenburg, D. , Pintelon, T. , Picioreanu, C. , Van Loosdrecht, M. , Johns, M. , 2009. Three-dimensional simulations of biofilm growth in porous media. AlChE J. 55 (2), 494–504 .
Seifert, D. , Engesgaard, P. , 2007. Use of tracer tests to investigate changes in flow and transport properties due to bioclogging of porous media. J. Contam. Hydrol. 93 (1), 58–71 .
Sen, R. , 2008. Biotechnology in petroleum recovery: the microbial eor. Prog. Energy Com- bust. Sci. 34 (6), 714–724 .
Seymour, J.D. , Gage, J.P. , Codd, S.L. , Gerlach, R. , 2004. Anomalous fluid transport in porous media induced by biofilm growth. Phys. Rev. Lett. 93 (19), 198103 . Seymour, J.D. , Gage, J.P. , Codd, S.L. , Gerlach, R. , 2007. Magnetic resonance microscopy
of biofouling induced scale dependent transport in porous media. Adv. Water Resour. 30 (6), 1408–1420 .
Stewart, T. L., Fogler, H. S., 2001. Biomass plug development and propagation in porous media.
Stoodley, P. , Lewandowski, Z. , Boyle, J.D. , Lappin-Scott, H.M. , 1999. Structural deforma- tion of bacterial biofilms caused by short-term fluctuations in fluid shear: an in situ investigation of biofilm rheology. Biotechnol. Bioeng. 65 (1), 83–92 .
Thormann, K.M. , Saville, R.M. , Shukla, S. , Pelletier, D.A. , Spormann, A.M. , 2004. Ini- tial phases of biofilm formation in shewanella oneidensis mr-1. J. Bacteriol. 186 (23), 8096–8104 .
Thormann, K.M. , Saville, R.M. , Shukla, S. , Spormann, A.M. , 2005. Induction of rapid de- tachment in shewanella oneidensis mr-1 biofilms. J. Bacteriol. 187 (3), 1014–1021 . Thullner, M. , 2010. Comparison of bioclogging effects in saturated porous media within
one-and two-dimensional flow systems. Ecol. Eng. 36 (2), 176–196 .
Tsai, D.-M., 1995. A fast thresholding selection procedure for multimodal and unimodal histograms. Pattern Recognit. Lett. 16 (6), 653–666.
https://doi.org/10.1016/0167-8655(95)80011-H .
Vandevivere, P. , Baveye, P. , 1992. Saturated hydraulic conductivity reduction caused by aerobic bacteria in sand columns. Soil Sci. Soc. Am. J. 56 (1), 1–13 .
Vandevivere, P. , Baveye, P. , Lozada, D.S. , DeLeo, P. , 1995. Microbial clogging of saturated soils and aquifer materials: evaluation of mathematical models. Water Resour. Res. 31 (9), 2173–2180 .
Venkateswaran, K. , Moser, D.P. , Dollhopf, M.E. , Lies, D.P. , Saffarini, D.A. , MacGre- gor, B.J. , Ringelberg, D.B. , White, D.C. , Nishijima, M. , Sano, H. , Burghardt, J. , Stacker- brandt, E. , Nealson, K.H. , 1999. Polyphasic taxonomy of the genus shewanella and description of shewanella oneidensis sp. nov.. Int. J. Syst. Evol. Microbiol. 49 (2), 705–724 .
Vogel, H.-J. , Weller, U. , Schlüter, S. , 2010. Quantification of soil structure based on minkowski functions. Comput. Geosci. 36 (10), 1236–1245 .
Vogt, S.J. , Sanderlin, A.B. , Seymour, J.D. , Codd, S.L. , 2013. Permeability of a growing biofilm in a porous media fluid flow analyzed by magnetic resonance displacemen- t-relaxation correlations. Biotechnol. Bioeng. 110 (5), 1366–1375 .
Wagner, M. , Taherzadeh, D. , Haisch, C. , Horn, H. , 2010. Investigation of the mesoscale structure and volumetric features of biofilms using optical coherence tomography. Biotechnol. Bioeng. 107 (5), 844–853 .
Wildenschild, D. , Sheppard, A.P. , 2013. X-ray imaging and analysis techniques for quan- tifying pore-scale structure and processes in subsurface porous medium systems. Adv. Water Resour. 51, 217–246 .
Xi, C. , Marks, D. , Schlachter, S. , Luo, W. , Boppart, S.A. , 2006. High-resolution three-di- mensional imaging of biofilm development using optical coherence tomography. J. Biomed. Opt. 11 (3) . 034001–034001
Yarwood, R. , Rockhold, M.L. , Niemet, M. , Selker, J.S. , Bottomley, P.J. , 2002. Noninva- sive quantitative measurement of bacterial growth in porous media under unsaturat- ed-flow conditions. Appl. Environ. Microbiol. 68 (7), 3597–3605 .
Young, J.C. , Dahab, M.F. , 1983. Effect of media design on the performance of fixed-bed anaerobic reactors. Water Sci. Technol. 15 (8–9), 369–383 .
