**DOI:**10.1128/AEM.03016-09

## ABSTRACT

Molecules become readily visible by magnetic resonance imaging (MRI) when labeled with a paramagnetic tag. Consequently, MRI can be used to image their transport through porous media. In this study, we demonstrated that this method could be applied to image mass transport processes in biofilms. The transport of a complex of gadolinium and diethylenetriamine pentaacetic acid (Gd-DTPA), a commercially available paramagnetic molecule, was imaged both in agar (as a homogeneous test system) and in a phototrophic biofilm. The images collected were *T*_{1} weighted, where *T*_{1} is an MRI property of the biofilm and is dependent on Gd-DTPA concentration. A calibration protocol was applied to convert *T*_{1} parameter maps into concentration 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 model revealed that transport of Gd-DTPA in agar was purely via diffusion, with a diffusion coefficient of 7.2 × 10^{−10} m^{2} 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 and advection, equivalent to a diffusion coefficient of 1.04 × 10^{−9} m^{2} s^{−1}. This technology can be used to further explore mass transport processes in biofilms, either by using the wide range of commercially available paramagnetically tagged molecules and nanoparticles or by using bespoke tagged molecules.

Biofilms are utilized in a wide range of biotechnological processes, such as cleansing municipal and industrial wastewater, bioremediation of hazardous waste sites, biofuel production, and the generation of electricity in microbial fuel cells (20, 31, 35). They also play an important role in mediating the geochemistry of the natural environment (35). Critically, our growing understanding of the biology, physics, and chemistry of biofilms is allowing us to manipulate biofilms and enhance their performance in a variety of biotechnologies (33). The optimization of biofilm processes is, however, hindered when a lack of quantitative measurements of critical biofilm parameters exists.

For the biofilm to function, the relevant substrates must be transported through the biofilm matrix, where they are metabolized. The rate at which these metabolites are transported through the biofilm can be critical in controlling the performance of the biofilm (5, 8, 13, 31). Equally, the rate at which the biofilm can sequester nonmetabolizable pollutants, such as nonmetabolizable heavy metals and recalcitrant organics, is also mediated by the transport rate (9, 28). Previous studies of mass transport inside biofilms show that transport occurs not only by diffusion but also by advection if the biofilm contains interconnected channels (5, 9, 13, 19, 39, 40, 45). When transported by diffusion, the mass of the diffusing solute plays a key role in mediating the transport rate. That is, the higher the molecular mass of the solute, the lower its diffusion coefficient (7, 39). Moreover, the molecular masses and diffusion rates of these solutes vary considerably, ranging from low-mass, fast-diffusing metabolites, such as H_{2} and O_{2}, to large, slowly diffusing organic macromolecules tens to hundreds of kDa in size. Indeed, high-molecular-mass molecules and nanoparticles are an important part of the substrate and pollutant load in both wastewater treatment and natural aquatic systems (21). At a certain size, large macromolecules and nanoparticles become too large to diffuse into the dense extracellular polymeric substance (EPS) matrix, although they still can be transported deep into the biofilm along open channels (9, 39).

Moreover, due to the heterogeneous nature of biofilms, substrates can also display significant spatial variation in mass transport rates, such as a decrease in transport rate with biofilm depth (4). As attempts to understand biofilm function or enhance biofilm performance are dependent upon accurate mass transport data sets, quantifying the transport behaviors of different-molecular-mass molecules in different biofilms is key to allowing us to model real biofilm systems more accurately.

Recognizing the importance of mass transport, researchers have already used a variety of methods, such as microelectrodes, confocal laser scanning microscopy (CLSM), fluorescence recovery after photobleaching (FRAP), and two-photon excitation microscopy to obtain mass transport data from biofilms (7, 11, 12). These approaches have provided invaluable data on mass transport within biofilms. However, as with any method, each has certain limitations. For example, microelectrodes are used to measure the mass transport of low-molecular-mass molecules; particulates and high-molecular-mass molecules are undetectable by this method. Moreover, the insertion of a probe is invasive and thus has potential to disrupt the surrounding material, altering results. This could be problematic when numerous insertions must be made, such as during spatial mapping of diffusion coefficients in heterogeneous biofilms. Conversely, CLSM is noninvasive. However, small molecules such as H_{2} or O_{2} cannot be labeled with the fluorescent probe, and thus only the transport of higher-molecular-weight compounds can be determined. This method, which relies on photons penetrating the biofilm, is limited both to biofilm thickness (<100 μm) and to its density due to optical scattering effects (26, 43). Although the two-photon excitation method can overcome the depth penetration limitation of CLSM by approximately four times (26), it is not suitable where biofilms exceed these thicknesses. FRAP also suffers similar thickness limitations and light-scattering effects. However, the capacity of magnetic resonance imaging (MRI) for completely noninvasive measurement of the transport of both low- and high-molecular-mass compounds and its ability to image inside hydrated biological matrices (1, 30), no matter what thickness, means that it has significant potential for mass transport analysis of biofilms and can thus be an invaluable additional tool in this research field.

Researchers have already used MRI to examine flow dynamics over biofilm surfaces (22, 37), metabolite consumption and production (23), the flux of heavy metals in metal-immobilizing bioreactors (15, 25), water diffusion in biofilms (28, 44), and the transport and fate of metals both in natural and artificial biofilms (28, 29) and in real methanogenic granules which are employed in anaerobic wastewater treatment (2).

## Principles of MRI.

MRI using the hydrogen nucleus (^{1}H) is ideal 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 from the nuclear magnetic resonance (NMR) of the hydrogen nucleus.

Some nuclei, including the hydrogen nucleus, possess both intrinsic spin angular momentum and a magnetic moment. The hydrogen nucleus is thus commonly referred to as a nuclear “spin.” When a sample is placed in the main magnetic field (*B*_{0}), the nuclear spins inside the sample have a slight tendency to align with the direction of the main magnetic field, conventionally termed the longitudinal direction. This polarizes the sample, inducing a net magnetization (*M _{z}*) along the longitudinal direction. Also, the spins precess about the axis of the main magnetic field, at a frequency of ω

_{0}= γ

*B*

_{0}, known as the Larmor frequency. The proportionality constant γ is known as the magnetogyric ratio and is a property of the nucleus. The precession of a nuclear spin in a magnetic field is analogous to the slow rotation of a tilted spinning top about the axis of the gravitational field.

The application of electromagnetic radiation that matches this precession frequency (commonly, radio frequency [RF]) can be used to manipulate these spins. The application of an RF pulse causes the net magnetization to rotate from its equilibrium position along the main magnetic field (*z* axis) onto the *xy* plane, producing a transverse magnetization (*M _{xy}*) which rotates around the

*z*direction. This rotating

*M*induces a current in the RF coil which is the MRI signal. The degree of rotation of the net magnetization from its equilibrium position is known as the flip angle, and this is controlled by the magnitude and the duration of the applied RF pulse (excitation pulse).

_{xy}Following excitation by an RF pulse, the spins will return to equilibrium; this process is called relaxation. The relaxation is described by two processes. Transverse relaxation is the loss of the transverse component, which is described by the relaxation time constant *T*_{2}, and longitudinal relaxation is the recovery of the longitudinal component, which is described by the relaxation time constant *T*_{1}.

Imaging is achieved by application of linear magnetic field gradients across the sample, causing spins at different spatial positions to experience slightly different magnetic fields and hence to precess at different frequencies, thus labeling their spatial positions.

## Application of MRI to this study.

Most MRI procedures utilize the ^{1}H NMR signal because H_{2}O is dominant in biological systems and the ^{1}H nucleus gives the largest NMR signal. This, however, means that mass transport analysis in biofilms is almost exclusively limited to the measurement of water mobility inside biofilms (18, 44). For other molecules, mass transport analysis is exceptionally difficult due to their much lower concentrations, which inhibits detection. Fortunately, water diffusivity can be used as a proxy for determining diffusivities of other low-molecular-mass molecules, as there is a close relationship between the diffusivities of water and low-molecular-mass molecules (3, 42, 44). However, as molecular mass increases, the diffusion coefficients of molecules compared to that of water differ by orders of magnitude, and water diffusivity becomes an increasingly less reliable proxy.

These macromolecules (compounds ranging from 1 kDa to hundreds of nanometers) cannot be ignored, as they contribute significantly to the pollutant load of wastewater and natural aquatic systems (21). Consequently, we must pursue alternative ways of determining mass transport of these important larger molecules by MRI.

The aim of this study is to demonstrate that this can be achieved by using molecules labeled with a paramagnetic metal. Molecules labeled with paramagnetic metals are readily visible by MRI and thus should enable *in vivo*, *in situ*, and real-time imaging of the transport of those macromolecules throughout a biofilm. This technology is already heavily utilized in medical diagnostic methods such as MRI of tumors, MR angiography, and myocardial perfusion (27, 38). This technology works not by imaging the paramagnetic molecule but by imaging its affect upon the relaxation times of the ^{1}H nuclei immediately surrounding it, thus creating sufficient contrast to the region being imaged.

In this study, a complex of gadolinium (a paramagnetic metal) with the chelating agent diethylenetriamine pentaacetic acid (Gd-DTPA) was used. This is a commonly used clinical MRI contrast agent. Not only does this agent provide strong contrast and is thus easy to image, it also is an exceptionally stable complex (log stability constant *K* = 20.5 [36]) and hence will not dissociate within the biofilm. Indeed, this high stability enables medical practitioners to inject Gd-DTPA into the human body without fear that the molecules will break down and release toxic Gd^{3+}. It is also one of the simplest commercially available paramagnetic complexes and one which is commonly used 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 of the spin lattice relaxation time (*T*_{1}) of surrounding ^{1}H nuclei because of the dipole-dipole interaction between the seven unpaired electrons of Gd^{3+} and the single proton of the hydrogen nucleus. Therefore, construction of spatially resolved *T*_{1} parameter maps during the mass transport of the Gd-labeled molecules reveals their movement through the biofilm. Moreover, the actual concentrations of the tracers can be determined, as *T*_{1} is inversely proportional to the concentration of the Gd-labeled molecules (6, 28, 38). Consequently, the effect of the paramagnetic label upon the MRI signal enables us to not only image the transport of these molecules but also spatially quantify their concentration in real time.

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

In this first study, we aimed to demonstrate the suitability of using paramagnetically tagged molecules for tracing mass transport in biofilms and hence its potential for mass transport analysis of a diverse range of mid- to high-molecular-mass molecules and nanoparticles within biofilm structures. Prior to applying this technology to the *Phormidium* biofilm, the technique was applied and validated with a simple system where the transport rate (diffusion coefficient) of Gd-DTPA was quantified inside an artificial biofilm composed simply of agar. The profiles of time-varying concentrations in agar were fitted to the solution of the one-dimensional diffusion equation to see if they were consistent with diffusive transport. Moreover, the results from the *Phormidium* biofilm experiment were compared 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 and allowed to cool such that it produced an agar tube with an approximate semicircular cross section (Fig. 1).

The phototrophic biofilm used in this study was 1 cm thick and composed of the cyanobacterium *Phormidium* sp. (strain PP03) from the culture collection of V. R. Phoenix (28). This phototrophic biofilm was grown in the laboratory in a tray containing BG-11 (with NaNO_{3}) nutrient medium (32) to a depth of 3 cm. This was inoculated with *Phormidium* and placed on a rocking machine at 10 rpm. This arrangement was then kept in an incubator and maintained at 28°C, with a constant light intensity of 25 μmol m^{2} s^{−1}.

Flow system.During the agar experiment, the flow cell containing the agar was positioned inside the MRI bore. The flow cell containing the agar was first connected via silicon tubing to an 18-MΩ water supply and slowly washed with ultrapure water at a rate of 7.5 cm/min using a peristaltic pump (Fig. 1). The system was then connected to a 4-liter reservoir of a 1.8 mM Gd-DTPA (molecular mass, 547 g/mol; Sigma Aldrich) solution, and the solution was pumped through the flow cell at a rate of 7.5 cm/min.

During the phototrophic biofilm experiment, the *Phormidium* biofilm was carefully positioned in a custom-made, circular, 2.2-cm-diameter plastic flow cell with 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 the biofilm (Fig. 2). The flow cell was then positioned inside the MRI bore. At this time, the flow cell containing the phototrophic biofilm was first connected via the silicon tubing to an 18-MΩ water supply and slowly washed with ultrapure water. The system was then connected to a 4-liter reservoir of a 5 mM Gd-DTPA solution, which was pumped over the biofilm at a rate of 7.5 cm/min.

MRI.The MRI experiments were performed on a Bruker Avance BioSpec system, using a 30-cm-bore, 7-T superconducting magnet (Bruker BioSpec, Karlsruhe, Germany). A Bruker microimaging gradient insert (model BG-6) and 200-A gradient amplifiers were used to provide strong linear magnetic field gradient pulses of up to 1,000 mT/m, thus allowing the system to perform microimaging experiments. A Bruker 35-mm-diameter birdcage RF volume resonator was used to excite and detect the ^{1}H signal.

Here, MRI was used to measure spatially and temporally resolved *T*_{1} values of both agar and *Phormidium* biofilm while Gd-DTPA was transported through these systems. The *T*_{1} value at different biofilm locations is influenced by a number of factors, including biofilm composition, water content, and the concentration of paramagnetic ions (Gd-DTPA). Collecting a *T*_{1}-based image of the biofilm prior to Gd-DTPA uptake reveals the impact of biofilm composition and water content on *T*_{1}. The change in *T*_{1} upon Gd-DTPA uptake is then known to be solely due to the Gd-DTPA. Thus, *T*_{1} values can be used to determine concentrations of Gd-DTPA. First, *T*_{1}-weighted images were measured with five different excitation pulse flip angles, which highlight only *T*_{1} image contrast. They were then used for calculation of *T*_{1} parameter maps, where the image intensity is the actual *T*_{1} value. These parameter maps were then used to obtain quantitative images of Gd-DTPA concentration.

Acquisition of *T*_{1}-weighted images.The transport of Gd-DTPA inside both agar and *Phormidium* biofilm was imaged by acquisition of *T*_{1}-weighted images in the axial plane by using a two-dimensional gradient echo pulse sequence, FLASH. Images were obtained across the samples, with a slice thickness of 1 mm. Both the agar and *Phormidium* biofilm experiments were performed with imaging parameters, with an echo time (*T _{E}*) of 4 ms and repetition times (

*T*) of 75 ms for agar and 20 ms for the biofilm. The field of view was 3 cm by 3 cm, using an imaging matrix of 200 by 200 pixels, giving an in-plane resolution of 150 μm by 150 μm. During both experiments,

_{R}*T*

_{1}-weighted images were acquired with five different excitation pulse flip angles (10°, 20°, 40°, 60°, and 90°). The imaging time with each flip angle was approximately 18 s, using a single-signal average.

Calculation of *T*_{1} parameter maps.In a gradient echo pulse sequence, the local signal intensity is given by the equation (16, 24).
$$mathtex$$\[S_{(t)}{=}S_{0_{(t)}}\ \left(\frac{1{-}e^{{-}T_{R}/T_{1}}}{1{-}\mathrm{cos}\ {\alpha}{\cdot}e^{{-}T_{R}/T_{1}}}\right)e^{{-}T_{E}/T_{2}{\ast}}\mathrm{sin}\ {\alpha}\]$$mathtex$$(1) where $$mathtex$$\(S_{0_{(t)}}\)$$mathtex$$is the available maximum signal intensity, α is the flip angle of the excitation pulse, *T _{R}* denotes the repetition time (the time interval between two successive excitation pulses),

*T*is the echo time (the time interval between the excitation and signal readout center),

_{E}*T*

_{1}is the longitudinal relaxation time, and

*T*

_{2}* is the apparent transverse relaxation time.

In equation 1, the term e^{−TE/T2*}is considered constant, since *T*_{E} was a predefined constant throughout the experiment and *T*_{2}* was assumed constant for a particular pixel at a particular time interval. Consequently, equation 1 can be reduced as
$$mathtex$$\[S_{(t)}{=}K\mathrm{sin}{\alpha}\ \left(\frac{1{-}e^{{-}T_{R}/T_{1}}}{1{-}\mathrm{cos}\ {\alpha}{\cdot}e^{{-}T_{R}/T_{1}}}\right)\]$$mathtex$$(2) where *K* is a constant which includes the terms S_{0(t)}and e^{−TE/T2*}.

*T*
_{1} parameter maps were calculated from the series of five *T*_{1}-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 angles were fitted to equation 2 using a nonlinear least-squares algorithm (Fig. 3B). This procedure estimates the values for the parameters *K* and *T*_{1} of that pixel. This procedure was applied to estimate the *T*_{1} value of every pixel within the slice (two-dimensional image) (Fig. 3C).

Calibration of Gd-DTPA concentrations from *T*_{1} parameter maps.The presence of paramagnetic metal, such as gadolinium, causes a concentration-dependent reduction in *T*_{1}. The effect of paramagnetic ions, such as Gd^{3+} (in Gd-DTPA), on the relaxation time of water's ^{1}H is represented by the equation (6, 28, 38)
$$mathtex$$\[[C]{=}\frac{1}{R}\ \left(\frac{1}{T_{1i}}{-}\frac{1}{T_{10}}\right)\]$$mathtex$$(3) where *T*_{10} is the relaxation time in the absence of Gd-DTPA, *T*_{1i} is the relaxation time 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, *T*_{10} and *T*_{1i} are known variables, as they are taken directly from *T*_{1} parameter maps. *R*, however, is unknown and must be separately determined in order to quantify the concentration measurements.

Determination of the relaxivity constant (*R*) of Gd-DTPA in agar and *Phormidium* biofilm.Recent investigations show that, when changes in the *T*_{1} relaxation times are used to quantify the available Gd-DTPA concentrations, the *R* value of Gd-DTPA depends on the solids content of the sample, with *R* increasing approximately linearly as the solids content increases (28, 38).

Thus, the effect of solids content on Gd-DTPA relaxivity in a *Phormidium* biofilm was investigated. Here, biofilm samples were prepared at four different solids contents by mixing the same amount of biofilm with four different volumes of Gd-DTPA solutions. At each solids content, six different samples were made with known Gd-DTPA concentrations (ranging from 0 to 5 mM). *T*_{1} values of all samples were measured. Then, plots of 1/*T*_{1i} versus Gd-DTPA concentration were made for samples with similar solids contents, and the *R* value for each solids content was determined by fitting equation 3 to their data using the linear least-squares method. The percentage of the solids content for each sample was determined by weighing the mixtures before and after drying to a constant weight at 60°C. Then, *R* values were plotted against solids contents and the linear relationship between *R* and solids contents was determined by fitting the data using the linear least-squares method. At the end of the Gd-DTPA transport experiment, the solids content of the *Phormidium* biofilm was determined by weighing the biofilm before and after drying the sample to a constant weight at 60°C. The appropriate *R* value corresponding to its solids content was then determined from the *R*-versus-solids content relationship described above. This *R* 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 experiment. This way of estimating the *R* value of the Gd-DTPA in the experimental biofilm enables the use of a value for *R* related to the solids content of the biofilm, 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 of Gd-DTPA. Then, 1/*T*_{1i} values were plotted against the concentration of Gd-DTPA, and the *R* value was estimated by fitting equation 3 to the data using the linear least-squares method.

Estimating the diffusion coefficient of Gd-DTPA inside agar.Concentration profiles along a straight line through the center of the flow cell (see Fig. 6F) were extracted from the data at six discrete points in time (3, 13, 23, 33, 43, and 53 min) during the first hour of the experiment. After 1 h, the Gd-DTPA had penetrated only the upper layers of the agar. Therefore, if diffusive transport dominates, then the effect of the flow cell boundaries and the irregular domain will be negligible on these central concentration profiles. This means that diffusion might be represented by a one-dimensional model of Fickian diffusion. To test this, we compared the profiles to a standard solution of the diffusion equation for a semi-infinite one-dimensional domain (10). If the concentration on the upper boundary of the agar is assumed to be constant through time (*C* = *C*_{0}) and the initial concentration in the remainder of the domain is zero, then the solution is given by
$$mathtex$$\[C(x,\ t){=}C_{0}\mathrm{erfc}(x/\sqrt{4Dt})\]$$mathtex$$(4) where erfc is the complementary error function, *D* is the diffusion coefficient of Gd-DTPA inside agar, and *t* is time. Nonlinear least-squares fitting of the data to this model allowed the diffusion coefficient to be calibrated.

Modeling the mass transport process of Gd-DTPA inside the *Phormidium* biofilm.To determine whether the concentration profiles of Gd-DTPA measured using MRI were commensurate with purely diffusion-driven transport, they were compared with those simulated for a mathematical model of diffusion. The morphology of the surface of the biofilm is variable in space, and therefore, it is not 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 along the axis of flow that enables us to use a two-dimensional diffusion model. A two-dimensional finite element model for diffusion of Gd-DTPA into the biofilm was implemented using COMSOL Multiphysics 3.4. Diffusion was simulated only within the biofilm, domain Ω shown in Fig. 4, which was determined from the MR image (see Fig. 8A). The boundary of the domain was split into two parts (Fig. 4) so that ∂Ω = Γ_{1} ∪ Γ_{2}, where Γ_{1} is the top surface of the biofilm and Γ_{2} includes the walls of the plastic holder and the surfaces of the gaskets, inside which biofilm was placed. The concentration of Gd-DTPA in the bulk liquid and hence on the boundary of Γ_{1} was assumed to be a constant, *C**, through time. No transport was permitted through walls and gasket boundaries, Γ_{2}.

Hence, the model was defined by
$$mathtex$$\[\frac{{\partial}C(x,\ y)}{{\partial}t}{=}{\nabla}{\cdot}[D{\nabla}C(x,\ y)]\mathrm{where}x,y{\in}{\Omega}\]$$mathtex$$(5)$$mathtex$$\[C(x,\ y){=}C{\ast}\mathrm{where}x,\ y{\in}{\Gamma}_{1}\]$$mathtex$$(6)$$mathtex$$\[\frac{{\partial}C(x,\ y)}{{\delta}{\bar{n}}}{=}0\mathrm{where}x,\ y{\in}{\Gamma}_{2}\]$$mathtex$$(7) Here, n̄ is the vector normal to the boundaries (Γ_{2}) and *D* is the diffusion coefficient, which we assume to be constant in time and space. The concentration in the bulk liquid, *C**, was 5 mM. For the purposes of the model, the diffusion coefficient was initially assumed to be the same as that calculated for the agar (7.2 × 10^{−10} m^{2} s^{−1}), as both agar and biofilm exhibit very similar solids contents. The same model was then used to estimate the diffusion coefficient of Gd-DTPA inside biofilm. Here, the diffusion coefficient was calibrated using a golden search algorithm in Matlab, which calls the COMSOL model a subroutine. The objective function was the sum of square errors between observed and simulated concentrations, and an optimum diffusion coefficient was estimated at the minimum value of this objective function.

The model was undertaken purely for comparative purposes to determine if transport was dominated by diffusion and to highlight any deviations from diffusion to help evaluate the MRI measurements. We did not develop the complexity 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 as the presence of EPS and compactness of the filaments, were investigated using freeze-substitution transmission electron microscopy (TEM), with samples prepared by the freeze-substitution method (41). Unlike processing the samples for TEM at room temperature, processing them with the freeze-substitution technique better preserves their structural information (17).

## RESULTS

Relaxivity constant (*R*) of Gd-DTPA inside agar.The variation of 1/*T*_{1i} values of agar samples with respect to the Gd-DTPA concentrations is shown in Fig. 5A. The relaxivity value of Gd-DTPA inside agar was estimated as 3.4 s^{−1} mM^{−1} by fitting the data to equation 3.

Relaxivity constant (*R*) of Gd-DTPA inside *Phormidium* biofilm.The variation of the relaxivity of Gd-DTPA with respect to the solids content of the *Phormidium* biofilm is shown in Fig. 5B. A linear least-squares fit to these data gives
$$mathtex$$\[R{=}1.7125S{+}6.5306\]$$mathtex$$(8) where *S* is the solids content of the biofilm. The solids content of the actual biofilm sample used during the flowthrough experiment was measured to be 1.2%, and from the above linear relationship (equation 8), the *R* value of that biofilm sample was estimated as 8.58 s^{−1} mM^{−1}. This was then used in equation 3 to determine the Gd-DTPA concentration inside the biofilm.

Diffusion of Gd-DTPA inside agar.In order to test the validity of this MRI method for imaging transport in biofilms, the transport of Gd-DTPA in a simpler, 1.5%-agar test system was imaged. The transport of Gd-DTPA into the agar was recorded by *T*_{1}-weighted images acquired with a 40° flip angle at time intervals of 23, 48, 73, 98, and 123 min, as shown in Fig. 6 A to E. The transport of Gd-DTPA is shown by the expansion of the brighter region into the agar, as diffusing Gd-DTPA molecules shortens the *T*_{1} value of the surrounding ^{1}H nuclei, hence increasing the measured MRI signal, which is shown brighter in a *T*_{1}-weighted image.

As the actual concentration of Gd-DTPA is inversely proportional to the *T*_{1} value, the calibration protocol (equation 3) was then used to convert the *T*_{1} parameter maps into actual Gd-DTPA concentration maps at time intervals of 23, 48, 73, 98, and 123 min, as shown in Fig. 6F to J. Again, the expansion of the brighter region into the biofilm shows the transport of Gd-DTPA. Concentration profiles along the transect shown by the white line (Fig. 6F) at time intervals of 3, 23, 53, and 103 min are shown in Fig. 7A.

By inspecting equation 4, it can be seen that if diffusive transport dominates and if concentrations along the same transect are plotted against the variable x/$$mathtex$$\(\sqrt{t}\)$$mathtex$$, all of the profiles should collapse onto a single curve. It can be seen from Fig. 7B that this is indeed the case, suggesting that Gd-DTPA was transported 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 of Gd-DTPA inside agar was 7.2 × 10^{−10} m^{2} s^{−1}. This gave an excellent goodness-of-fit value (*R*^{2} = 0.97).

Transport of Gd-DTPA into the *Phormidium* biofilm.The transport of Gd-DTPA into the *Phormidium* biofilm was recorded by *T*_{1}-weighted images acquired with a 40° flip angle, as shown in Fig. 8A to E, at time intervals of 2, 22, 72, 122, and 172 min. Again, the transport of Gd-DTPA is shown by the expansion of the brighter region into the biofilm.

The calibration protocol was then used to convert the *T*_{1} parameter maps into actual Gd-DTPA concentration maps at time intervals of 2, 22, 72, 122, and 172 min, as shown in Fig. 8F to J. Again, the expansion of the brighter region into the biofilm shows the transport of Gd-DTPA. Figure 8K to O show the two-dimensional model generated using a diffusion coefficient of 7.2 × 10^{−10} m^{2} s^{−1}, the value calibrated from diffusive transport through agar. Figure 9A shows the comparison of concentration profiles of experimental data along the transect shown by the white line in Fig. 8F, with model data along the same transect as that in Fig. 8K. The model using the diffusion coefficient from agar shows slightly slower transport than the experimental data, indicating that transport in the biofilm is faster than in agar. When the model was calibrated to the concentration profiles, the best fit (*R*^{2} = 0.92) was achieved with a diffusion coefficient of 1.04 × 10^{−9} m^{2} s^{−1}, as shown in Fig. 9B.

Freeze-substitution transmission electron microscopy analysis of biofilm structure.The structural complexity of *Phormidium* biofilm was visualized using freeze-substitution transmission electron microscopy, as illustrated in Fig. 10. A transmission electron micrograph (Fig. 10A) shows that *Phormidium* filaments are embedded in an EPS matrix, and this was observed in most areas of the biofilm. However, in some areas, there was little or no EPS between the filaments, as shown in Fig. 10B, thus creating voids and interconnected channels between filaments.

## DISCUSSION

In this study, MRI was successful in quantitatively measuring the 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 examine the suitability of the approach. Results from both the agar and *Phormidium* biofilm experiments were then compared with simple one- and two-dimensional models.

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 corroborates the suitability of this MRI method, as such homogeneous diffusion is expected in a homogeneous agar gel. Moreover, the calculated diffusion coefficient of 7.2 × 10^{−10} m^{2} s^{−1} is an acceptable estimate for the diffusivity of Gd-DTPA (molecular mass, 547 g/mol). This is slower than that of much lighter molecules, such as water (*D* = 2.2 × 10^{−9} m^{2} s^{−1}), yet faster than a similar but heavier Gd-tagged molecule, Magnevist (*D* = 2.6 × 10^{−10} m^{2} 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 of Gd-DTPA into the *Phormidium* biofilm. A simple two-dimensional diffusion model that employed the diffusion coefficient calibrated for agar did not match the experimental results (Fig. 9A); transport appears to be quicker in the biofilm. When the diffusion model was calibrated against the concentration profiles in the biofilm, the best-fitting model (Fig. 9B) was achieved with a diffusion coefficient of 1.04 × 10^{−9} m^{2} s^{−1}. We suggest that this is an unrealistically high rate of diffusion for Gd-DTPA in the biofilm, since the diffusion coefficient of Gd-DTPA inside the agar is only 7.2 × 10^{−10} m^{2} s^{−1}. The agar is a highly permeable, inert gel designed to give minimal resistance to diffusive transport. Consequently, the diffusion coefficient determined in agar is expected to be the maximum unrestricted value. Thus, it appears that the transport of Gd-DTPA in the biofilm is not by diffusion alone. It should be noted here that the thick filamentous biofilm formed by *Phormidium* is a heterogeneous, complex three-dimensional system. TEM of the biofilm's internal structure reveals that, in most areas, a dense EPS matrix fills the spaces between *Phormidium* filaments (Fig. 10A). However, in other areas, there is very little or no EPS filling these spaces (Fig. 10B), thus creating voids and interconnected channels. Previous studies show that these structural heterogeneities found in biofilms can increase the transport of solutes into and through biofilms via advection (5, 12, 13, 39, 40). Therefore, the component of advective transport of Gd-DTPA in the *Phormidium* biofilm increased its transport rate over and above its calculated diffusion coefficient in agar.

Despite the fact that transport in the biofilm is not solely diffusive, the calibrated model is a reasonable match to the observed data. This has been observed in biofilm mass transport studies using other techniques where calculated diffusion coefficients are higher than those possible by pure diffusion (12). Thus, the effective diffusion coefficients described in this and other biofilm studies not only embody the impact of factors such as porosity and tortuosity on diffusion but also can embody components of advection. These effective parameters can be a useful means of quantifying the effects of different transport mechanisms without explicitly representing all of the heterogeneities and flow pathways through a porous medium. The presence of small voids and interconnected channels inside this biofilm cannot be imaged by MRI in this study, as the achievable resolution was 150 μm, which is larger than the size of most voids and channels found inside biofilms (13). Ultimately, however, as our ability to image transport at increasingly high spatial resolutions evolves, it may be possible to disentangle flow mechanisms in a few laboratory-based experiments if the sizes of voids and interconnected channels are compatible with achievable higher resolutions using MRI. However, for quantifying biofilm transport for any practical applications, it may always be necessary to use effective parameters in prudently simplified transport models. Therefore, the transport of Gd-DTPA into this *Phormidium* biofilm can be characterized with an effective diffusion coefficient which comprises both its diffusional and advectional transport properties.

Usually during the maturation process, biofilms adapt to optimize their mass transport behaviors (4). Therefore, conducting mass transport experiments under unidirectional flow (as in the flow cell) may produce differing mass transport behaviors of a biofilm grown under bidirectional flow (on a rocking table). However, these differences do not impact the overall aim of this study, which is to demonstrate that paramagnetic tracers can be used to track mass transport in biofilms.

As described earlier, the diffusion of Gd-DTPA is illustrated by the expansion of the brighter region in *T*_{1}-weighted images and in the concentration maps (Fig. 8). However, as Gd-DTPA uptake increased, a small darker region was observed at the top of the biofilm in the *T*_{1}-weighted images (Fig. 8A to E) which continued to expand with time. This is likely a side effect of increasing Gd-DTPA concentration upon the signal intensity. Normally, signal intensity is proportional to the concentration of paramagnetic ions (higher concentrations cause higher signal intensities). However, above a certain threshold concentration, paramagnetic ions can cause a rapid reduction in the signal intensity (24, 34). Apparently, the highest concentrations of Gd-DTPA in the biofilm system are above this threshold and thus generate a darkening, rather than brightening, in the top of the biofilm in the *T*_{1}-weighted images. Importantly, Gd-DTPA concentrations are not calculated directly from these single-flip-angle *T*_{1}-weighted images. For each image pixel, the signal intensity, *S*_{(t)}, with multiple flip angles is fitted to equation 2 using a nonlinear least-squares algorithm. Thus, the darkening seen in the *T*_{1}-weighted images does not result in an incorrect calculation of lower Gd-DTPA concentration in the top of the biofilm (Fig. 9). Although not problematic, this darkening can be overcome by reducing the Gd-DTPA concentration in the in-flow solution so that the paramagnetic-ion concentration stays below the threshold.

The few dark pixels seen in the very top of the biofilm in the concentration maps (Fig. 8F to J) likely result from the higher error that is associated with calculating Gd-DTPA concentrations at higher, rather than lower, concentrations. This is because the relationship between *T*_{1} and Gd-DTPA concentration is inversely proportional (equation 3); thus, changes in concentration at high Gd-DTPA concentrations cause much smaller shifts in *T*_{1} than at low concentrations.

The resolution gained during this study is 150 μm. This is useful for very thick biofilms, which are more common in the natural environment. The thicknesses of biofilms which are commonly used in engineered systems range from many tens of microns to millimeters, and thus a higher resolution is required. The resolution of the MR image is limited by the attainable signal-to-noise ratio. The signal-to-noise ratio increase is inversely proportional to the diameter of the RF coil, which detects the MR signal. In this study, a commercially available 35-mm-diameter RF coil was used. Smaller-diameter RF coils, however, are capable of generating higher resolutions. Indeed, smaller-diameter bespoke RF coils have already been used to examine metabolite production and consumption in biofilms ∼100 μm thick, with a resolution of ∼20 μm (23, 37). Evidently, the next step here should be to build smaller-diameter RF coils which will enable the imaging of paramagnetically labeled molecules in thinner biofilms.

Overall, this study illustrates the suitability of this approach in biofilm research to quantify the mass transport rates and pathways of different macromolecules inside biofilm systems. Indeed, a wide range of commercially available paramagnetically tagged molecules and nanoparticles are available to explore the impact of parameters such as molecular mass, charge, and molecular geometry or structure on transport in different biofilms. These range from Gd-DTPA (molecular mass, 547 g/mol) to large macromolecules, such as gadolinium-labeled albumin (∼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 ultrasmall superparamagnetic iron oxide (USPIO) can also be used. It is also possible to construct bespoke, tagged molecules with specific properties.

Therefore, the use of MRI with paramagnetic tracers has the potential to significantly improve our understanding of the way pollutants and substrates are transported and transformed by real biofilms.

## ACKNOWLEDGMENTS

This work was funded by a Lord Kelvin and Adam Smith Scholarship, University of Glasgow, and by an Engineering and Physical Sciences 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 assistance with TEM.

## FOOTNOTES

- Received 14 December 2009.
- Accepted 21 April 2010.

- Copyright © 2010 American Society for Microbiology