APPLIED AND ENVIRONMENTAL MICROBIOLOGY, June 2010, p. 4027–4036 Vol. 76, No. 120099-2240/10/$12.00 doi:10.1128/AEM.03016-09Copyright © 2010, American Society for Microbiology. All Rights Reserved.

Application of Paramagnetically Tagged Molecules for MagneticResonance Imaging of Biofilm Mass Transport Processes�

B. Ramanan,1,2,3 W. M. Holmes,2 W. T. Sloan,3 and V. R. Phoenix1*Department of Geographical and Earth Sciences, Gregory Building, University of Glasgow, Glasgow G12 8QQ, United Kingdom1;

GEMRIC, Wellcome Surgical Institute, Faculty of Medicine, University of Glasgow, Glasgow G61 1QH, United Kingdom2;and Department of Civil Engineering, Rankine Building, University of Glasgow, Glasgow G12 8QQ, United Kingdom3

Received 14 December 2009/Accepted 21 April 2010

Molecules become readily visible by magnetic resonance imaging (MRI) when labeled with a paramagnetictag. Consequently, MRI can be used to image their transport through porous media. In this study, wedemonstrated that this method could be applied to image mass transport processes in biofilms. The transportof a complex of gadolinium and diethylenetriamine pentaacetic acid (Gd-DTPA), a commercially availableparamagnetic molecule, was imaged both in agar (as a homogeneous test system) and in a phototrophicbiofilm. The images collected were T1 weighted, where T1 is an MRI property of the biofilm and is dependenton Gd-DTPA concentration. A calibration protocol was applied to convert T1 parameter maps into concen-tration maps, thus revealing the spatially resolved concentrations of this tracer at different time intervals.Comparing the data obtained from the agar experiment with data from a one-dimensional diffusion modelrevealed that transport of Gd-DTPA in agar was purely via diffusion, with a diffusion coefficient of 7.2 � 10�10

m2 s�1. In contrast, comparison of data from the phototrophic biofilm experiment with data from a two-dimensional diffusion model revealed that transport of Gd-DTPA inside the biofilm was by both diffusion andadvection, equivalent to a diffusion coefficient of 1.04 � 10�9 m2 s�1. This technology can be used to furtherexplore mass transport processes in biofilms, either by using the wide range of commercially availableparamagnetically tagged molecules and nanoparticles or by using bespoke tagged molecules.

Biofilms are utilized in a wide range of biotechnologicalprocesses, such as cleansing municipal and industrial wastewa-ter, bioremediation of hazardous waste sites, biofuel produc-tion, and the generation of electricity in microbial fuel cells(20, 31, 35). They also play an important role in mediating thegeochemistry of the natural environment (35). Critically, ourgrowing understanding of the biology, physics, and chemistryof biofilms is allowing us to manipulate biofilms and enhancetheir performance in a variety of biotechnologies (33). Theoptimization of biofilm processes is, however, hindered when alack of quantitative measurements of critical biofilm parame-ters exists.

For the biofilm to function, the relevant substrates must betransported through the biofilm matrix, where they are metab-olized. The rate at which these metabolites are transportedthrough the biofilm can be critical in controlling the perfor-mance of the biofilm (5, 8, 13, 31). Equally, the rate at whichthe biofilm can sequester nonmetabolizable pollutants, such asnonmetabolizable heavy metals and recalcitrant organics, isalso mediated by the transport rate (9, 28). Previous studies ofmass transport inside biofilms show that transport occurs notonly by diffusion but also by advection if the biofilm containsinterconnected channels (5, 9, 13, 19, 39, 40, 45). When trans-ported by diffusion, the mass of the diffusing solute plays a keyrole in mediating the transport rate. That is, the higher themolecular mass of the solute, the lower its diffusion coefficient

(7, 39). Moreover, the molecular masses and diffusion rates ofthese solutes vary considerably, ranging from low-mass, fast-diffusing metabolites, such as H2 and O2, to large, slowly dif-fusing organic macromolecules tens to hundreds of kDa in size.Indeed, high-molecular-mass molecules and nanoparticles arean important part of the substrate and pollutant load in bothwastewater treatment and natural aquatic systems (21). At acertain size, large macromolecules and nanoparticles becometoo large to diffuse into the dense extracellular polymeric sub-stance (EPS) matrix, although they still can be transporteddeep into the biofilm along open channels (9, 39).

Moreover, due to the heterogeneous nature of biofilms, sub-strates can also display significant spatial variation in masstransport rates, such as a decrease in transport rate with bio-film depth (4). As attempts to understand biofilm function orenhance biofilm performance are dependent upon accuratemass transport data sets, quantifying the transport behaviors ofdifferent-molecular-mass molecules in different biofilms is keyto allowing us to model real biofilm systems more accurately.

Recognizing the importance of mass transport, researchershave already used a variety of methods, such as microelec-trodes, confocal laser scanning microscopy (CLSM), fluores-cence recovery after photobleaching (FRAP), and two-photonexcitation microscopy to obtain mass transport data from bio-films (7, 11, 12). These approaches have provided invaluabledata on mass transport within biofilms. However, as with anymethod, each has certain limitations. For example, microelec-trodes are used to measure the mass transport of low-molec-ular-mass molecules; particulates and high-molecular-massmolecules are undetectable by this method. Moreover, theinsertion of a probe is invasive and thus has potential to disruptthe surrounding material, altering results. This could be prob-

* Corresponding author. Mailing address: Department of Geo-graphical and Earth Sciences, Gregory Building, University of Glas-gow, Glasgow G12 8QQ, United Kingdom. Phone: 44 (0)141 330 5474.Fax: 44 (0)141 330 4894. E-mail: Vernon.Phoenix@ges.gla.ac.uk.

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lematic when numerous insertions must be made, such as dur-ing spatial mapping of diffusion coefficients in heterogeneousbiofilms. Conversely, CLSM is noninvasive. However, smallmolecules such as H2 or O2 cannot be labeled with the fluo-rescent probe, and thus only the transport of higher-molecular-weight compounds can be determined. This method, whichrelies on photons penetrating the biofilm, is limited both tobiofilm thickness (�100 �m) and to its density due to opticalscattering effects (26, 43). Although the two-photon excitationmethod can overcome the depth penetration limitation ofCLSM by approximately four times (26), it is not suitablewhere biofilms exceed these thicknesses. FRAP also sufferssimilar thickness limitations and light-scattering effects. How-ever, the capacity of magnetic resonance imaging (MRI) forcompletely noninvasive measurement of the transport of bothlow- and high-molecular-mass compounds and its ability toimage inside hydrated biological matrices (1, 30), no matterwhat thickness, means that it has significant potential for masstransport analysis of biofilms and can thus be an invaluableadditional tool in this research field.

Researchers have already used MRI to examine flow dynam-ics over biofilm surfaces (22, 37), metabolite consumption andproduction (23), the flux of heavy metals in metal-immobilizingbioreactors (15, 25), water diffusion in biofilms (28, 44), andthe transport and fate of metals both in natural and artificialbiofilms (28, 29) and in real methanogenic granules which areemployed in anaerobic wastewater treatment (2).

Principles of MRI. MRI using the hydrogen nucleus (1H) isideal for studying hydrated biological tissue (such as biofilms)due to the abundance of hydrogen nuclei in this material,notably from water. Here, the MRI signal is generated fromthe nuclear magnetic resonance (NMR) of the hydrogen nu-cleus.

Some nuclei, including the hydrogen nucleus, possess bothintrinsic spin angular momentum and a magnetic moment. Thehydrogen nucleus is thus commonly referred to as a nuclear“spin.” When a sample is placed in the main magnetic field(B0), the nuclear spins inside the sample have a slight tendencyto align with the direction of the main magnetic field, conven-tionally termed the longitudinal direction. This polarizes thesample, inducing a net magnetization (Mz) along the longitu-dinal direction. Also, the spins precess about the axis of themain magnetic field, at a frequency of �0 � �B0, known as theLarmor frequency. The proportionality constant � is known asthe magnetogyric ratio and is a property of the nucleus. Theprecession of a nuclear spin in a magnetic field is analogous tothe slow rotation of a tilted spinning top about the axis of thegravitational field.

The application of electromagnetic radiation that matchesthis precession frequency (commonly, radio frequency [RF])can be used to manipulate these spins. The application of anRF pulse causes the net magnetization to rotate from its equi-librium position along the main magnetic field (z axis) onto thexy plane, producing a transverse magnetization (Mxy) whichrotates around the z direction. This rotating Mxy induces acurrent in the RF coil which is the MRI signal. The degree ofrotation of the net magnetization from its equilibrium positionis known as the flip angle, and this is controlled by the mag-nitude and the duration of the applied RF pulse (excitationpulse).

Following excitation by an RF pulse, the spins will return toequilibrium; this process is called relaxation. The relaxation isdescribed by two processes. Transverse relaxation is the loss ofthe transverse component, which is described by the relaxationtime constant T2, and longitudinal relaxation is the recovery ofthe longitudinal component, which is described by the relax-ation time constant T1.

Imaging is achieved by application of linear magnetic fieldgradients across the sample, causing spins at different spatialpositions to experience slightly different magnetic fields andhence to precess at different frequencies, thus labeling theirspatial positions.

Application of MRI to this study. Most MRI proceduresutilize the 1H NMR signal because H2O is dominant in bio-logical systems and the 1H nucleus gives the largest NMRsignal. This, however, means that mass transport analysis inbiofilms is almost exclusively limited to the measurement ofwater mobility inside biofilms (18, 44). For other molecules,mass transport analysis is exceptionally difficult due to theirmuch lower concentrations, which inhibits detection. Fortu-nately, water diffusivity can be used as a proxy for determiningdiffusivities of other low-molecular-mass molecules, as there isa close relationship between the diffusivities of water and low-molecular-mass molecules (3, 42, 44). However, as molecularmass increases, the diffusion coefficients of molecules com-pared to that of water differ by orders of magnitude, and waterdiffusivity becomes an increasingly less reliable proxy.

These macromolecules (compounds ranging from 1 kDa tohundreds of nanometers) cannot be ignored, as they contributesignificantly to the pollutant load of wastewater and naturalaquatic systems (21). Consequently, we must pursue alterna-tive ways of determining mass transport of these importantlarger molecules by MRI.

The aim of this study is to demonstrate that this can beachieved by using molecules labeled with a paramagneticmetal. Molecules labeled with paramagnetic metals are readilyvisible by MRI and thus should enable in vivo, in situ, andreal-time imaging of the transport of those macromoleculesthroughout a biofilm. This technology is already heavily uti-lized in medical diagnostic methods such as MRI of tumors,MR angiography, and myocardial perfusion (27, 38). This tech-nology works not by imaging the paramagnetic molecule but byimaging its affect upon the relaxation times of the 1H nucleiimmediately surrounding it, thus creating sufficient contrast tothe region being imaged.

In this study, a complex of gadolinium (a paramagneticmetal) with the chelating agent diethylenetriamine pentaaceticacid (Gd-DTPA) was used. This is a commonly used clinicalMRI contrast agent. Not only does this agent provide strongcontrast and is thus easy to image, it also is an exceptionallystable complex (log stability constant K � 20.5 [36]) and hencewill not dissociate within the biofilm. Indeed, this high stabilityenables medical practitioners to inject Gd-DTPA into the hu-man body without fear that the molecules will break down andrelease toxic Gd3�. It is also one of the simplest commerciallyavailable paramagnetic complexes and one which is commonlyused to tag other large molecules.

The presence of Gd-labeled molecules, such as Gd-DTPA,at any point inside a biofilm will cause noticeable shortening ofthe spin lattice relaxation time (T1) of surrounding 1H nuclei

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because of the dipole-dipole interaction between the sevenunpaired electrons of Gd3� and the single proton of the hy-drogen nucleus. Therefore, construction of spatially resolvedT1 parameter maps during the mass transport of the Gd-la-beled molecules reveals their movement through the biofilm.Moreover, the actual concentrations of the tracers can be de-termined, as T1 is inversely proportional to the concentrationof the Gd-labeled molecules (6, 28, 38). Consequently, theeffect of the paramagnetic label upon the MRI signal enablesus to not only image the transport of these molecules but alsospatially quantify their concentration in real time.

For this pilot study, we utilized a laboratory-grown 1-cm-thick phototrophic biofilm (composed of the cyanobacteriumPhormidium sp. strain PP03). This was chosen as a simplemodel biofilm, as Phormidium biofilm readily grows in thelaboratory and phototrophic biofilms of this thickness occur inthe natural environment.

In this first study, we aimed to demonstrate the suitability ofusing paramagnetically tagged molecules for tracing masstransport in biofilms and hence its potential for mass transportanalysis of a diverse range of mid- to high-molecular-massmolecules and nanoparticles within biofilm structures. Prior toapplying this technology to the Phormidium biofilm, the tech-nique was applied and validated with a simple system wherethe transport rate (diffusion coefficient) of Gd-DTPA wasquantified inside an artificial biofilm composed simply of agar.The profiles of time-varying concentrations in agar were fittedto the solution of the one-dimensional diffusion equation tosee if they were consistent with diffusive transport. Moreover,the results from the Phormidium biofilm experiment were com-pared with those of a simple two-dimensional model.

MATERIALS AND METHODS

Agar and phototrophic biofilms. The artificial biofilm was made up of agar(1.5%). Molten agar was poured into a modified 30-ml plastic syringe andallowed to cool such that it produced an agar tube with an approximate semi-circular cross section (Fig. 1).

The phototrophic biofilm used in this study was 1 cm thick and composed ofthe cyanobacterium Phormidium sp. (strain PP03) from the culture collection ofV. R. Phoenix (28). This phototrophic biofilm was grown in the laboratory in atray containing BG-11 (with NaNO3) nutrient medium (32) to a depth of 3 cm.This was inoculated with Phormidium and placed on a rocking machine at 10rpm. This arrangement was then kept in an incubator and maintained at 28°C,with a constant light intensity of 25 �mol m2 s�1.

Flow system. During the agar experiment, the flow cell containing the agar waspositioned inside the MRI bore. The flow cell containing the agar was firstconnected via silicon tubing to an 18-M� water supply and slowly washed withultrapure water at a rate of 7.5 cm/min using a peristaltic pump (Fig. 1). Thesystem was then connected to a 4-liter reservoir of a 1.8 mM Gd-DTPA (mo-lecular mass, 547 g/mol; Sigma Aldrich) solution, and the solution was pumpedthrough the flow cell at a rate of 7.5 cm/min.

During the phototrophic biofilm experiment, the Phormidium biofilm wascarefully positioned in a custom-made, circular, 2.2-cm-diameter plastic flow cellwith a special gasket arrangement such that only the top surface of the biofilm

was in contact with the flowing solution. This ensured that transport of Gd-DTPA into the biofilm could take place only from the top to the bottom of thebiofilm (Fig. 2). The flow cell was then positioned inside the MRI bore. At thistime, the flow cell containing the phototrophic biofilm was first connected via thesilicon tubing to an 18-M� water supply and slowly washed with ultrapure water.The system was then connected to a 4-liter reservoir of a 5 mM Gd-DTPAsolution, which was pumped over the biofilm at a rate of 7.5 cm/min.

MRI. The MRI experiments were performed on a Bruker Avance BioSpecsystem, using a 30-cm-bore, 7-T superconducting magnet (Bruker BioSpec,Karlsruhe, Germany). A Bruker microimaging gradient insert (model BG-6) and200-A gradient amplifiers were used to provide strong linear magnetic fieldgradient pulses of up to 1,000 mT/m, thus allowing the system to performmicroimaging experiments. A Bruker 35-mm-diameter birdcage RF volume res-onator was used to excite and detect the 1H signal.

Here, MRI was used to measure spatially and temporally resolved T1 values ofboth agar and Phormidium biofilm while Gd-DTPA was transported throughthese systems. The T1 value at different biofilm locations is influenced by anumber of factors, including biofilm composition, water content, and the con-centration of paramagnetic ions (Gd-DTPA). Collecting a T1-based image of thebiofilm prior to Gd-DTPA uptake reveals the impact of biofilm composition andwater content on T1. The change in T1 upon Gd-DTPA uptake is then known tobe solely due to the Gd-DTPA. Thus, T1 values can be used to determineconcentrations of Gd-DTPA. First, T1-weighted images were measured with fivedifferent excitation pulse flip angles, which highlight only T1 image contrast. Theywere then used for calculation of T1 parameter maps, where the image intensityis the actual T1 value. These parameter maps were then used to obtain quanti-tative images of Gd-DTPA concentration.

Acquisition of T1-weighted images. The transport of Gd-DTPA inside bothagar and Phormidium biofilm was imaged by acquisition of T1-weighted imagesin the axial plane by using a two-dimensional gradient echo pulse sequence,FLASH. Images were obtained across the samples, with a slice thickness of 1mm. Both the agar and Phormidium biofilm experiments were performed withimaging parameters, with an echo time (TE) of 4 ms and repetition times (TR) of75 ms for agar and 20 ms for the biofilm. The field of view was 3 cm by 3 cm, usingan imaging matrix of 200 by 200 pixels, giving an in-plane resolution of 150 �mby 150 �m. During both experiments, T1-weighted images were acquired withfive different excitation pulse flip angles (10°, 20°, 40°, 60°, and 90°). The imagingtime with each flip angle was approximately 18 s, using a single-signal average.

Calculation of T1 parameter maps. In a gradient echo pulse sequence, thelocal signal intensity is given by the equation (16, 24).

St � S0t� 1 � e�TR/T1

1 � cos � � e�TR/T1�e�TE/T2*sin � (1)

where S0t is the available maximum signal intensity, � is the flip angle of theexcitation pulse, TR denotes the repetition time (the time interval between twosuccessive excitation pulses), TE is the echo time (the time interval between theexcitation and signal readout center), T1 is the longitudinal relaxation time, andT2* is the apparent transverse relaxation time.

In equation 1, the term e�TE/T2* is considered constant, since TE was a predefinedconstant throughout the experiment and T2* was assumed constant for a particularpixel at a particular time interval. Consequently, equation 1 can be reduced as

St � K sin �� 1 � e�TR/T1

1 � cos � � e�TR/T1� (2)

where K is a constant which includes the terms S0t and e�TE/T2*.T1 parameter maps were calculated from the series of five T1-weighted images

which were acquired with different flip angles (10°, 20°, 40°, 60°, 90°) (Fig. 3A).For each image pixel, the MRI signal intensities, S(t), with different flip angleswere fitted to equation 2 using a nonlinear least-squares algorithm (Fig. 3B). Thisprocedure estimates the values for the parameters K and T1 of that pixel. This

FIG. 1. Schematic of the flow cell containing agar. Cross sectionsare along the flow cell (a) and across the flow cell (b).

FIG. 2. Schematic of the flow cell containing Phormidium biofilm.Cross sections are along the flow cell (a) and across the flow cell (b).

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procedure was applied to estimate the T1 value of every pixel within the slice(two-dimensional image) (Fig. 3C).

Calibration of Gd-DTPA concentrations from T1 parameter maps. The pres-ence of paramagnetic metal, such as gadolinium, causes a concentration-depen-dent reduction in T1. The effect of paramagnetic ions, such as Gd3� (in Gd-DTPA), on the relaxation time of water’s 1H is represented by the equation (6,28, 38)

�C �1R� 1

T1i�

1T10� (3)

where T10 is the relaxation time in the absence of Gd-DTPA, T1i is the relaxationtime in the presence of Gd-DTPA, [C] denotes the concentration of the Gd-DTPA, and R is the relaxivity constant of the Gd-DTPA.

In the current study, T10 and T1i are known variables, as they are taken directlyfrom T1 parameter maps. R, however, is unknown and must be separately de-termined in order to quantify the concentration measurements.

Determination of the relaxivity constant (R) of Gd-DTPA in agar and Phor-midium biofilm. Recent investigations show that, when changes in the T1 relax-ation times are used to quantify the available Gd-DTPA concentrations, the Rvalue of Gd-DTPA depends on the solids content of the sample, with R increas-ing approximately linearly as the solids content increases (28, 38).

Thus, the effect of solids content on Gd-DTPA relaxivity in a Phormidiumbiofilm was investigated. Here, biofilm samples were prepared at four differentsolids contents by mixing the same amount of biofilm with four different volumesof Gd-DTPA solutions. At each solids content, six different samples were madewith known Gd-DTPA concentrations (ranging from 0 to 5 mM). T1 values of allsamples were measured. Then, plots of 1/T1i versus Gd-DTPA concentrationwere made for samples with similar solids contents, and the R value for eachsolids content was determined by fitting equation 3 to their data using the linearleast-squares method. The percentage of the solids content for each sample wasdetermined by weighing the mixtures before and after drying to a constant weightat 60°C. Then, R values were plotted against solids contents and the linearrelationship between R and solids contents was determined by fitting the datausing the linear least-squares method. At the end of the Gd-DTPA transportexperiment, the solids content of the Phormidium biofilm was determined byweighing the biofilm before and after drying the sample to a constant weight at60°C. The appropriate R value corresponding to its solids content was thendetermined from the R-versus-solids content relationship described above. ThisR value was used in equation 3 to calculate the Gd-DTPA concentrations inside

the biofilm from the MRI data collected during the Gd-DTPA transport exper-iment. This way of estimating the R value of the Gd-DTPA in the experimentalbiofilm enables the use of a value for R related to the solids content of thebiofilm, thus giving a more accurate measurement of Gd-DTPA concentration.

In order to estimate the R value of Gd-DTPA inside the artificial biofilm(agar), agar samples were prepared with five different known concentrations ofGd-DTPA. Then, 1/T1i values were plotted against the concentration of Gd-DTPA, and the R value was estimated by fitting equation 3 to the data using thelinear least-squares method.

Estimating the diffusion coefficient of Gd-DTPA inside agar. Concentrationprofiles along a straight line through the center of the flow cell (see Fig. 6F) wereextracted from the data at six discrete points in time (3, 13, 23, 33, 43, and 53min) during the first hour of the experiment. After 1 h, the Gd-DTPA hadpenetrated only the upper layers of the agar. Therefore, if diffusive transportdominates, then the effect of the flow cell boundaries and the irregular domainwill be negligible on these central concentration profiles. This means that diffu-sion might be represented by a one-dimensional model of Fickian diffusion. Totest this, we compared the profiles to a standard solution of the diffusion equa-tion for a semi-infinite one-dimensional domain (10). If the concentration on theupper boundary of the agar is assumed to be constant through time (C � C0) andthe initial concentration in the remainder of the domain is zero, then the solutionis given by

Cx, t � C0erfcx/�4Dt (4)

where erfc is the complementary error function, D is the diffusion coefficient ofGd-DTPA inside agar, and t is time. Nonlinear least-squares fitting of the datato this model allowed the diffusion coefficient to be calibrated.

Modeling the mass transport process of Gd-DTPA inside the Phormidiumbiofilm. To determine whether the concentration profiles of Gd-DTPA mea-sured using MRI were commensurate with purely diffusion-driven transport, theywere compared with those simulated for a mathematical model of diffusion. Themorphology of the surface of the biofilm is variable in space, and therefore, it isnot possible to represent the transport by a one-dimensional diffusion equation.However, there is a degree of symmetry in the shape of the biofilm surface alongthe axis of flow that enables us to use a two-dimensional diffusion model. Atwo-dimensional finite element model for diffusion of Gd-DTPA into the biofilmwas implemented using COMSOL Multiphysics 3.4. Diffusion was simulated onlywithin the biofilm, domain � shown in Fig. 4, which was determined from theMR image (see Fig. 8A). The boundary of the domain was split into two parts(Fig. 4) so that �� � �1 � �2, where �1 is the top surface of the biofilm and �2

includes the walls of the plastic holder and the surfaces of the gaskets, insidewhich biofilm was placed. The concentration of Gd-DTPA in the bulk liquid andhence on the boundary of �1 was assumed to be a constant, C*, through time. Notransport was permitted through walls and gasket boundaries, �2.

Hence, the model was defined by

�Cx, y

�t� � � �D�Cx, y where x, y � � (5)

Cx, y � C* where x, y � �1 (6)

FIG. 3. (A) For the slice across the biofilm, T1-weighted images areacquired with five different flip angles. (B) For each pixel, the variationof signal intensity, S(t), with respect to the flip angle, �, was fitted toequation 2, giving a T1 value. (C) Taking the T1 value of each pixelyields a T1 parameter map.

FIG. 4. Illustration of the two-dimensional model of the Phor-midium biofilm constructed using COMSOL Multiphysics. Dimensionsare in centimeters.

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�Cx, y

�n� 0 where x, y � �2 (7)

Here, n� is the vector normal to the boundaries (�2) and D is the diffusioncoefficient, which we assume to be constant in time and space. The concentrationin the bulk liquid, C*, was 5 mM. For the purposes of the model, the diffusioncoefficient was initially assumed to be the same as that calculated for the agar(7.2 � 10�10 m2 s�1), as both agar and biofilm exhibit very similar solidscontents. The same model was then used to estimate the diffusion coefficient ofGd-DTPA inside biofilm. Here, the diffusion coefficient was calibrated using agolden search algorithm in Matlab, which calls the COMSOL model a subrou-tine. The objective function was the sum of square errors between observed andsimulated concentrations, and an optimum diffusion coefficient was estimated atthe minimum value of this objective function.

The model was undertaken purely for comparative purposes to determine iftransport was dominated by diffusion and to highlight any deviations from dif-fusion to help evaluate the MRI measurements. We did not develop the com-plexity of the model further here, as this is beyond the scope of this paper.

Visualization of structural complexity of Phormidium biofilm using freeze-substitution TEM. The structural complexity of the Phormidium biofilm, such asthe presence of EPS and compactness of the filaments, were investigated usingfreeze-substitution transmission electron microscopy (TEM), with samples pre-pared by the freeze-substitution method (41). Unlike processing the samples forTEM at room temperature, processing them with the freeze-substitution tech-nique better preserves their structural information (17).

RESULTS

Relaxivity constant (R) of Gd-DTPA inside agar. The vari-ation of 1/T1i values of agar samples with respect to the Gd-DTPA concentrations is shown in Fig. 5A. The relaxivity valueof Gd-DTPA inside agar was estimated as 3.4 s�1 mM�1 byfitting the data to equation 3.

Relaxivity constant (R) of Gd-DTPA inside Phormidium bio-film. The variation of the relaxivity of Gd-DTPA with respectto the solids content of the Phormidium biofilm is shown in Fig.5B. A linear least-squares fit to these data gives

R � 1.7125S � 6.5306 (8)

where S is the solids content of the biofilm. The solids contentof the actual biofilm sample used during the flowthrough ex-periment was measured to be 1.2%, and from the above linearrelationship (equation 8), the R value of that biofilm samplewas estimated as 8.58 s�1 mM�1. This was then used in equa-

tion 3 to determine the Gd-DTPA concentration inside thebiofilm.

Diffusion of Gd-DTPA inside agar. In order to test the va-lidity of this MRI method for imaging transport in biofilms, thetransport of Gd-DTPA in a simpler, 1.5%-agar test system wasimaged. The transport of Gd-DTPA into the agar was recordedby T1-weighted images acquired with a 40° flip angle at timeintervals of 23, 48, 73, 98, and 123 min, as shown in Fig. 6A toE. The transport of Gd-DTPA is shown by the expansion of thebrighter region into the agar, as diffusing Gd-DTPA moleculesshortens the T1 value of the surrounding 1H nuclei, henceincreasing the measured MRI signal, which is shown brighterin a T1-weighted image.

As the actual concentration of Gd-DTPA is inversely pro-portional to the T1 value, the calibration protocol (equation 3)was then used to convert the T1 parameter maps into actualGd-DTPA concentration maps at time intervals of 23, 48, 73,98, and 123 min, as shown in Fig. 6F to J. Again, the expansionof the brighter region into the biofilm shows the transport ofGd-DTPA. Concentration profiles along the transect shown bythe white line (Fig. 6F) at time intervals of 3, 23, 53, and 103min are shown in Fig. 7A.

By inspecting equation 4, it can be seen that if diffusivetransport dominates and if concentrations along the sametransect are plotted against the variable x/�t, all of the profilesshould collapse onto a single curve. It can be seen from Fig. 7Bthat this is indeed the case, suggesting that Gd-DTPA wastransported by diffusion. The theoretical curve (equation 4)was fitted to the observed data using the nonlinear least-squares method, and the best-fitting diffusion coefficient ofGd-DTPA inside agar was 7.2 � 10�10 m2 s�1. This gave anexcellent goodness-of-fit value (R2 � 0.97).

Transport of Gd-DTPA into the Phormidium biofilm. Thetransport of Gd-DTPA into the Phormidium biofilm was re-corded by T1-weighted images acquired with a 40° flip angle, asshown in Fig. 8A to E, at time intervals of 2, 22, 72, 122, and172 min. Again, the transport of Gd-DTPA is shown by theexpansion of the brighter region into the biofilm.

The calibration protocol was then used to convert the T1

FIG. 5. (A) Variation of 1/T1i values with respect to Gd-DTPA concentration inside agar samples. (B) Variation of Gd-DTPA relaxivity withrespect to the solids contents of several Phormidium biofilm samples.

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parameter maps into actual Gd-DTPA concentration maps attime intervals of 2, 22, 72, 122, and 172 min, as shown in Fig.8F to J. Again, the expansion of the brighter region into thebiofilm shows the transport of Gd-DTPA. Figure 8K to O showthe two-dimensional model generated using a diffusion coeffi-cient of 7.2 � 10�10 m2 s�1, the value calibrated from diffusivetransport through agar. Figure 9A shows the comparison ofconcentration profiles of experimental data along the transectshown by the white line in Fig. 8F, with model data along thesame transect as that in Fig. 8K. The model using the diffusioncoefficient from agar shows slightly slower transport than theexperimental data, indicating that transport in the biofilm isfaster than in agar. When the model was calibrated to theconcentration profiles, the best fit (R2 � 0.92) was achievedwith a diffusion coefficient of 1.04 � 10�9 m2 s�1, as shown inFig. 9B.

Freeze-substitution transmission electron microscopy anal-ysis of biofilm structure. The structural complexity of Phor-

midium biofilm was visualized using freeze-substitution trans-mission electron microscopy, as illustrated in Fig. 10. Atransmission electron micrograph (Fig. 10A) shows that Phor-midium filaments are embedded in an EPS matrix, and this wasobserved in most areas of the biofilm. However, in some areas,there was little or no EPS between the filaments, as shown inFig. 10B, thus creating voids and interconnected channels be-tween filaments.

DISCUSSION

In this study, MRI was successful in quantitatively measuringthe time-varying, spatially distributed concentration of Gd-DTPA as it was transported into agar and Phormidium biofilm.The agar system was used as a simple test system to examinethe suitability of the approach. Results from both the agar andPhormidium biofilm experiments were then compared withsimple one- and two-dimensional models.

FIG. 6. Diffusion of Gd-DTPA into agar was recorded by T1-weighted images acquired with a 40° flip angle (A to E), and the calibrationprotocol (equation 3) was then used to convert the T1 parameter maps into actual Gd-DTPA concentration maps (F to J) at time intervals of 23,48, 73, 98, and 123 min. The gray scale indicates the Gd-DTPA concentrations (mM) inside the agar. The white line indicates a transect along whichconcentrations at 3, 23, 53, and 103 min are shown in Fig. 7A.

FIG. 7. (A) Calibrated Gd-DTPA concentrations at time intervals of 3, 23, 53, and 103 min along the transect shown by the white dotted linein Fig. 6F. (B) Calibrated Gd-DTPA concentration profiles during the first hour of the experiment (3, 13, 23, 33, 43, and 53 min), plotted againstdistance/�time and curve fitted to the solution of the Fickian one-dimensional diffusion equation to determine the diffusion coefficient of Gd-DTPAinside agar.

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As illustrated in Fig. 7B, concentration profiles for Gd-DTPA transport in agar collapsed well onto a single line.Critically, this indicates that transport is consistent with (i)diffusion and (ii) diffusion at a constant rate. This corroboratesthe suitability of this MRI method, as such homogeneous dif-fusion is expected in a homogeneous agar gel. Moreover, thecalculated diffusion coefficient of 7.2 � 10�10 m2 s�1 is anacceptable estimate for the diffusivity of Gd-DTPA (molecularmass, 547 g/mol). This is slower than that of much lightermolecules, such as water (D � 2.2 � 10�9 m2 s�1), yet faster

than a similar but heavier Gd-tagged molecule, Magnevist (D� 2.6 � 10�10 m2 s�1; molecular mass, 938 g/mol) (14).

This then enabled us to move on to a real biofilm system.Again, this MRI approach successfully tracked the transport ofGd-DTPA into the Phormidium biofilm. A simple two-dimen-sional diffusion model that employed the diffusion coefficientcalibrated for agar did not match the experimental results (Fig.9A); transport appears to be quicker in the biofilm. When thediffusion model was calibrated against the concentration pro-files in the biofilm, the best-fitting model (Fig. 9B) was

FIG. 8. Transport of Gd-DTPA into the Phormidium biofilm illustrated as T1-weighted images acquired with a 40° flip angle (A to E), calibratedGd-DTPA concentration maps (F to J), and diffusion model results (K to O) at time intervals of 2, 22, 72, 122, and 172 min. The gray scale indicatesthe Gd-DTPA concentrations (mM) inside the biofilm.

FIG. 9. Gd-DTPA transports inside the Phormidium biofilm are compared between experimental and model data (modeled at a diffusioncoefficient of 7.2 � 10�10 m2/s) (A) and between experimental and calibrated diffusion model data (B). Gd-DTPA concentration profiles werealong the transect shown by the white line in Fig. 8F and K at time intervals of 129, 429, 737, 1,038, and 1,341 s. Symbols represent experimentaldata, and solid lines represent model data at respective time intervals.

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achieved with a diffusion coefficient of 1.04 � 10�9 m2 s�1. Wesuggest that this is an unrealistically high rate of diffusion forGd-DTPA in the biofilm, since the diffusion coefficient of Gd-DTPA inside the agar is only 7.2 � 10�10 m2 s�1. The agar isa highly permeable, inert gel designed to give minimal resis-tance to diffusive transport. Consequently, the diffusion coef-ficient determined in agar is expected to be the maximumunrestricted value. Thus, it appears that the transport of Gd-DTPA in the biofilm is not by diffusion alone. It should benoted here that the thick filamentous biofilm formed by Phor-midium is a heterogeneous, complex three-dimensional sys-tem. TEM of the biofilm’s internal structure reveals that, inmost areas, a dense EPS matrix fills the spaces between Phor-midium filaments (Fig. 10A). However, in other areas, there isvery little or no EPS filling these spaces (Fig. 10B), thus cre-ating voids and interconnected channels. Previous studies showthat these structural heterogeneities found in biofilms can in-crease the transport of solutes into and through biofilms viaadvection (5, 12, 13, 39, 40). Therefore, the component ofadvective transport of Gd-DTPA in the Phormidium biofilmincreased its transport rate over and above its calculated dif-fusion coefficient in agar.

Despite the fact that transport in the biofilm is not solelydiffusive, the calibrated model is a reasonable match to theobserved data. This has been observed in biofilm mass trans-port studies using other techniques where calculated diffusioncoefficients are higher than those possible by pure diffusion(12). Thus, the effective diffusion coefficients described in thisand other biofilm studies not only embody the impact of fac-tors such as porosity and tortuosity on diffusion but also canembody components of advection. These effective parameterscan be a useful means of quantifying the effects of differenttransport mechanisms without explicitly representing all of theheterogeneities and flow pathways through a porous medium.The presence of small voids and interconnected channels in-side this biofilm cannot be imaged by MRI in this study, as the

achievable resolution was 150 �m, which is larger than the sizeof most voids and channels found inside biofilms (13). Ulti-mately, however, as our ability to image transport at increas-ingly high spatial resolutions evolves, it may be possible todisentangle flow mechanisms in a few laboratory-based exper-iments if the sizes of voids and interconnected channels arecompatible with achievable higher resolutions using MRI.However, for quantifying biofilm transport for any practicalapplications, it may always be necessary to use effective param-eters in prudently simplified transport models. Therefore, thetransport of Gd-DTPA into this Phormidium biofilm can becharacterized with an effective diffusion coefficient which com-prises both its diffusional and advectional transport properties.

Usually during the maturation process, biofilms adapt tooptimize their mass transport behaviors (4). Therefore, con-ducting mass transport experiments under unidirectional flow(as in the flow cell) may produce differing mass transportbehaviors of a biofilm grown under bidirectional flow (on arocking table). However, these differences do not impact theoverall aim of this study, which is to demonstrate that para-magnetic tracers can be used to track mass transport in bio-films.

As described earlier, the diffusion of Gd-DTPA is illustratedby the expansion of the brighter region in T1-weighted imagesand in the concentration maps (Fig. 8). However, as Gd-DTPAuptake increased, a small darker region was observed at thetop of the biofilm in the T1-weighted images (Fig. 8A to E)which continued to expand with time. This is likely a side effectof increasing Gd-DTPA concentration upon the signal inten-sity. Normally, signal intensity is proportional to the concen-tration of paramagnetic ions (higher concentrations causehigher signal intensities). However, above a certain thresholdconcentration, paramagnetic ions can cause a rapid reductionin the signal intensity (24, 34). Apparently, the highest concen-trations of Gd-DTPA in the biofilm system are above thisthreshold and thus generate a darkening, rather than bright-

FIG. 10. Transmission electron micrograph of a freeze-substituted Phormidium biofilm sample. (A) Cross section of Phormidium filamentsembedded in an EPS matrix. The EPS is the fine meshwork seen between cells. (B) Areas where there is little or no EPS between the filaments,thus with voids and interconnected channels between filaments.

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ening, in the top of the biofilm in the T1-weighted images.Importantly, Gd-DTPA concentrations are not calculated di-rectly from these single-flip-angle T1-weighted images. Foreach image pixel, the signal intensity, S(t), with multiple flipangles is fitted to equation 2 using a nonlinear least-squaresalgorithm. Thus, the darkening seen in the T1-weighted imagesdoes not result in an incorrect calculation of lower Gd-DTPAconcentration in the top of the biofilm (Fig. 9). Although notproblematic, this darkening can be overcome by reducing theGd-DTPA concentration in the in-flow solution so that theparamagnetic-ion concentration stays below the threshold.

The few dark pixels seen in the very top of the biofilm in theconcentration maps (Fig. 8F to J) likely result from the highererror that is associated with calculating Gd-DTPA concentra-tions at higher, rather than lower, concentrations. This is be-cause the relationship between T1 and Gd-DTPA concentra-tion is inversely proportional (equation 3); thus, changes inconcentration at high Gd-DTPA concentrations cause muchsmaller shifts in T1 than at low concentrations.

The resolution gained during this study is 150 �m. This isuseful for very thick biofilms, which are more common in thenatural environment. The thicknesses of biofilms which arecommonly used in engineered systems range from many tens ofmicrons to millimeters, and thus a higher resolution is re-quired. The resolution of the MR image is limited by theattainable signal-to-noise ratio. The signal-to-noise ratio in-crease is inversely proportional to the diameter of the RF coil,which detects the MR signal. In this study, a commerciallyavailable 35-mm-diameter RF coil was used. Smaller-diameterRF coils, however, are capable of generating higher resolu-tions. Indeed, smaller-diameter bespoke RF coils have alreadybeen used to examine metabolite production and consumptionin biofilms �100 �m thick, with a resolution of �20 �m (23,37). Evidently, the next step here should be to build smaller-diameter RF coils which will enable the imaging of paramag-netically labeled molecules in thinner biofilms.

Overall, this study illustrates the suitability of this approachin biofilm research to quantify the mass transport rates andpathways of different macromolecules inside biofilm systems.Indeed, a wide range of commercially available paramagneti-cally tagged molecules and nanoparticles are available to ex-plore the impact of parameters such as molecular mass, charge,and molecular geometry or structure on transport in differentbiofilms. These range from Gd-DTPA (molecular mass, 547g/mol) to large macromolecules, such as gadolinium-labeledalbumin (�74 kDa) and Gd nanoparticles (http://www.biopal.com/MRI.htm). While Gd-based tracers are most common,iron oxide-based paramagnetic contrast agents, such as ultra-small superparamagnetic iron oxide (USPIO) can also be used.It is also possible to construct bespoke, tagged molecules withspecific properties.

Therefore, the use of MRI with paramagnetic tracers has thepotential to significantly improve our understanding of the waypollutants and substrates are transported and transformed byreal biofilms.

ACKNOWLEDGMENTS

This work was funded by a Lord Kelvin and Adam Smith Scholar-ship, University of Glasgow, and by an Engineering and Physical Sci-ences Research Council grant (EP/G028443/1).

We thank Jim Mullen for his assistance with the MRI experiments.We thank Laurence Tetley and Margaret Mullen for their assistancewith TEM.

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