Quantifying Elastic Properties of Environmental Biofilms using Optical Coherence Elastography

Summary

This paper highlights the optical coherence elastography (OCE) technique's efficacy in rapidly and non-destructively characterizing biofilm elastic properties. We elucidate critical OCE implementation procedures for accurate measurements and present Young's modulus values for two granular biofilms.

Abstract

Biofilms are complex biomaterials comprising a well-organized network of microbial cells encased in self-produced extracellular polymeric substances (EPS). This paper presents a detailed account of the implementation of optical coherence elastography (OCE) measurements tailored for the elastic characterization of biofilms. OCE is a non-destructive optical technique that enables the local mapping of the microstructure, morphology, and viscoelastic properties of partially transparent soft materials with high spatial and temporal resolution. We provide a comprehensive guide detailing the essential procedures for the correct implementation of this technique, along with a methodology to estimate the bulk Young's modulus of granular biofilms from the collected measurements. These consist of the system setup, data acquisition, and postprocessing. In the discussion, we delve into the underlying physics of the sensors used in OCE and explore the fundamental limitations regarding the spatial and temporal scales of OCE measurements. We conclude with potential future directions for advancing the OCE technique to facilitate elastic measurements of environmental biofilms.

Introduction

In wastewater treatment and water resource recovery, beneficial biofilms in attached growth reactors are increasingly employed to enable microbes to convert undesirable pollutants, such as organic matter, nitrogen, and phosphate, into stabilized forms that can be easily removed from the water¹. In these systems, the biofilm's emergent function, namely biochemical transformations, is closely associated with the diversity of microbes residing in it and the nutrients these microbes receive². Accordingly, ongoing biofilm growth can pose a challenge to maintaining consistent reactor functionality because the new biofilm growth may alter the biofilm's overall metabolic processes, mass transfer characteristics, and community composition. Stabilizing the biofilm environment as much as possible can protect against such changes³. This includes ensuring a consistent flow of nutrients and keeping the structure of the biofilm stable with a steady thickness⁴. Monitoring the biofilm's stiffness and physical structure would enable researchers to gain insight into the overall health and functioning of the biofilm.

Biofilms exhibit viscoelastic properties^5,6,7. This viscoelastic nature results in a combination of an instantaneous and slow, time-dependent deformation in response to external mechanical forces. One unique aspect of biofilms is that, when they are subjected to substantial deformation, they respond like viscous liquids. Conversely, when subjected to minor deformation, their response is comparable to solids⁵. Moreover, within this small-deformation region, there is a deformation range under which biofilms exhibit a linear force-displacement relationship^5,6,7. Deformations within this linear range are optimal for assessing biofilm mechanical characteristics because these yield reproducible measurements. Several techniques can quantify the elastic response within this range. Optical coherence elastography (OCE) is an emerging technique that is being adapted for analyzing biofilms in this linear range (strains on the order of 10^-4-10^-5)^8,9.

OCE's most established application so far is in the biomedical field, where the technique has been applied to characterize biological tissues that only require superficial optical access. For example, Li et al. used OCE to characterize the elastic properties of skin tissue¹⁰. Other authors characterized the anisotropic elastic properties of porcine and human corneal tissues and how they are affected by intraocular pressure^{11,12,13,14,15,16}. Some advantages of the OCE method for studying biofilms are that it is non-destructive and provides mesoscale spatial resolution, it does not require any sample preparation, and the method itself is rapid; it provides co-registered measurements of physical structure and elastic properties (e.g., porosity, surface roughness, and morphology)^8,9,17,18.

The OCE method measures the local displacement of propagating elastic waves in a specimen using phase-sensitive optical coherence tomography (OCT). OCT is a low-coherence optical interferometer that transforms local changes in the sample displacement into an intensity change that is recorded with an optical spectrometer. The OCT technique has also been utilized in biofilm research for the characterization of mesoscale structure, porosity distribution in three dimensions, and biofilm deformation^17,19,20,21. In addition, Picioreanu et al. estimated biofilm mechanical properties using fluid-structure interaction inverse modeling of OCT cross-sectional deformation images²².

On the other hand, OCE measurements, coupled with inverse elastodynamic wave modeling, yield the wave speed of elastic waves in the sample, which enables the characterization of the elastic and viscoelastic properties of the sample. Our group adapted the OCE technique for quantitative measurement of biofilm elastic and viscoelastic properties^8,9,18 and validated the technique against shear rheometry measurements in agarose gel plate samples¹⁸. The OCE approach provides precise and reliable estimates of the biofilm properties since the measured elastic wave speed is correlated with the elastic properties of the sample. Furthermore, the spatial decay of the elastic wave amplitude can be directly correlated with the viscoelastic properties due to viscous effects in the material. We have reported OCE measurements of viscoelastic properties of mixed culture bacterial biofilms grown on coupons in a rotating annular reactor (RAR) and granular biofilms with complex geometries using elastodynamic wave models¹⁸.

The OCE technique is also a powerful alternative to traditional rheometry¹⁸which is used for viscoelastic characterization. Rheometry methods are best suited for samples with planar geometry. As such, granular biofilms, which have arbitrary shapes and surface morphologies, cannot be accurately characterized on a rheometer^8,23. In addition, unlike OCE, rheometry methods may be challenging to adapt for real-time measurements, for example, during biofilm growth in flow cells^24,25.

In this paper, we show that OCE measurements of the frequency-independent wave speed of surface waves can be used to characterize the biofilm elastic properties without the need for complicated models. This development will make the OCE approach more accessible to the broader biofilm community for studying the biofilm mechanical properties.

Figure 1 shows a schematic illustration of the OCT system used in this study. The system incorporates several instruments, including a commercial spectral-domain phase-sensitive OCT system, a delay generator, a function generator, and a piezoelectric transducer. The OCT system operates on the principle of interferometry by employing a broadband light source with a center wavelength of 930 nm. The collected light intensity, which is correlated with intricate structural details in the sample, is analyzed in the postprocessing unit and then converted to a cross-sectional image of the sample - commonly referred to as an OCT image. The OCT imaging depth depends on the severity of the optical scattering in the sample that stems from local variation in the refractive index and is limited to 1- 3 mm in biological tissues and biofilms. Since the optical phase in the sample and the interference intensity are modulated by motion, the OCT can be used to detect the local sample displacement. We leverage the displacement sensitivity of the OCT in the OCE method to track the steady state displacement field of elastic waves in the sample. Specifically, the function generator outputs a sinusoidal voltage to drive the piezoelectric transducer. The transducer, in turn, stretches and contracts with an oscillatory time history. The oscillatory displacement of the transducer imparts a sinusoidal force on the sample surface through a 3D-printed wedge tip at the apex of the transducer, leading to the generation of harmonic elastic waves in the sample. The wedge tip makes light contact with the sample, such that the sample remains intact after the actuator is retracted from the sample surface. To record the local displacement in the sample, adjacent depth scans separated by a fixed time delay are acquired at each pixel in the sample. The optical phase difference between consecutive scans at each pixel point is proportional to the local vertical displacement at the same point. Synchronization between the displacement of the transducer and the scanning optics in the OCT system is achieved through a trigger pulse that originates from the function generator and is delayed in the delay generator. This synchronization step facilitates the acquisition of consistent cross-sectional images of the local optical phase distribution in the sample. These images are directly proportional to the local vertical harmonic displacement in the sample and are known as the OCE image. OCE images are acquired at different transducer actuation frequencies to obtain the elastic wavelength and wave speed as a function of frequency. The wave speeds measured are analyzed with an elastodynamic model to determine the elastic properties of the sample.

Protocol

1. System setup

1. Gather the system components which include the commercial OCT system (base unit, stand, imaging head, and computer), waveform generator, transducer, delay/pulse generator, a switch with BNC connections, BNC cables and adapters, optical posts, and clamps.
2. Connect the sync signal from the function generator to a switch. Connect the other port of the switch to the delay generator.
3. Connect the output of the function generator to the transducer leads.
4. Connect the outputs of the delay generator to the trigger channel at the back of the OCT base unit. The output signal from the delay generator is a trigger pulse to initiate the motion of the scanning optics in the OCT system.
5. Turn on the system components (OCT base unit, computer, function generator, and delay generator) and launch the OCT software.
6. Configure the delay generator to send a transistor-transistor logic trigger signal to the OCT base unit. Refer to the OCT system manual for the trigger signal requirements.
7. Position the transducer beneath the OCT lens. The transducer has a 3D-printed wedge tip glued onto one of its ends that serves as a line source for elastic waves.

2. Image acquisition

1. On the OCT software, select the Doppler Acquisition Mode and enable the external trigger.
2. Place the granular biofilm under the lens in a sample holder and move it towards the tip of the transducer using a translation stage. Ensure that the transducer makes gentle contact with the sample surface, as shown in Figure 2. We used two granular biofilms (also known as granular sludge) with different nominal diameters (4.3 mm and 3.3 mm). This selection was made to investigate the impact of biofilm size on its mechanical properties. These were commercially obtained.
   NOTE: The sample holder employed in this study consists of a 3D-printed plastic plate with multiple hemispherical indentations. This holder does not allow for measurements under native conditions. Therefore, we introduced water from the natural environment during measurements to prevent the sample from drying.
3. Specify the scan region by clicking the Start and Endpoints of the Line of Interest (wave propagation path) in the sample monitor window. Center this line with respect to the transducer tip and ensure it is perpendicular to the edge of the tip.
4. Specify the number of pixels along the scan region and the depth of the sample and increase the number of B-scans (2D cross-sectional images) to be recorded to improve the signal-to-noise ratio of the OCE images. The presented results were obtained using 1523 pixels along the scanning path and 1024 pixels along the depth. A total of 50 B-scans were taken.
5. Click the Scan button and turn ON the switch. The OCT and OCE images should appear on the screen. Activate the switch within the trigger timeout time and the scan preparation time.
6. Ensure that the reference intensity is within the optimum range and position the sample within the focal region of the OCT microscope objective. A properly focused sample should have its top edge close to the top of the image.
7. Adjust the phase contour in the OCE image on the display toolbar by increasing the higher value of the left-hand side color bar and decreasing the lower value of the right-hand side color bar. This will increase the fringe contrast.
8. Configure the function generator to produce a single-frequency sinusoidal voltage by pressing the Sine button in the front panel and specify the starting excitation frequency for the measurements. The measurements in this study start at 4 kHz and end at 9.6 kHz. Enable the Output connector by pressing the Output key.
9. Set an acceptable voltage for the measurement. This value should maximize fringe visibility but also avoid phase wrapping. For the biofilms in this study and the frequency range of the measurements, a voltage between 5 and 10 V typically results in a phase map with good contrast.
10. Acquire the OCT and OCE images by clicking the Record button.
11. Repeat the measurements at different frequencies to obtain cross-sectional images of the elastic wave field with different wavelengths (or fringe periods).

3. Image Analysis

1. Obtain the physical size of the pixels. The physical pixel size in x is obtained by dividing the field of view in the x direction by the image size in the x direction and then multiplying by a factor of two. The physical pixel size in z is obtained by dividing the field of view in the z direction by the image size in the z direction. The field of view and image size values are stored in the structure array with the image information which can be accessed with the OCTFileOpen function provided in the MATLAB SDK in the ThorImageOCT package.
2. Obtain the OCT and OCE matrices using the OCTFileGetIntensity and OCTFileGetPhase functions, respectively, and take the average of the recorded frames. These functions are provided in the MATLAB SDK in the ThorImageOCT package.
3. Obtain the pixel locations of the top edge of the sample by binarizing the image and detecting the white pixels from top to bottom for each column.
4. Extract the phase distribution of the OCE image along this edge using the improfile function and compute the cumulative arc length in real dimensions. Compute the arc length by taking the cumulative sum of the norm of scaled differences between consecutive points in the x and z directions.
5. Compute the spatial fast Fourier transform of the measured OCT phase distribution (i.e., from the OCE images) with respect to the cumulative arc length using the plomb function.
6. Determine the location of the peak in the spectrum. This location represents the spatial frequency of the wave. Calculate the wave speed (or phase velocity) from the ratio of the transducer excitation frequency (units of Hz) and the spatial frequency (unit of inverse length).

Results

In this study, we used granular biofilms (also known as granular sludge), which were commercially obtained. Granules are spherical biofilms that form through self-aggregation, meaning that they do not require a carrier or surface on which to grow²⁶. Figure 3A shows a representative cross-sectional OCT image that arises due to the spatial variation of the local refractive index in a granular biofilm. The biofilm has a nominal diameter of 3 mm. Some of ...

Discussion

The attainable imaging depth in the OCT system is determined by the degree of light penetration from the light source, which depends on the wavelength of the source. Moreover, the wavelength determines the axial resolution. Longer wavelengths can penetrate more deeply into the sample but at the expense of reduced axial resolution compared to shorter wavelengths. Transverse resolution, on the other hand, is dependent on both the numerical aperture of the system and the wavelength, with shorter wavelengths delivering ...

Materials

Name	Company	Catalog Number	Comments
3D printed sample holder
3D printed wedge tip			3 mm width
BNC cables	Any brand
Delay generator	Stanford Research Systems	DG535	DG535 Digital delay/ Pulse Generator
Function generator	Agilent Technologies		33250A 80 MHz Function / Arbitrary Waveform Generator
Granular biofilm	Aqua-Aerobic Systems		Obtained from an Aerobic Granular Sludge reactor (Aqua-Aerobic Systems, Inc.)
MATLAB	MathWorks		Release 2022a (MATLAB 9.12)
Piezoelectric transducer	Thorlabs	PK2JUP1	Discrete Piezo Stack, 75 V, 30.0 µm Displacement
SD-OCT System	Thorlabs		Ganymede II, LSM03 scan lens
ThorImageOCT	Thorlabs		Version: 5.5.5