Laser speckle imaging for early detection of microbial colony forming units.

In this study, an optical contactless laser speckle imaging technique for the early identification of bacterial colony-forming units was tested. The aim of this work is to compare the laser speckle imaging method for the early assessment of microbial activity with standard visual inspection under white light illumination. In presented research, the growth of Vibrio natriegens bacterial colonies on the solid medium was observed and analyzed. Both - visual examination under white light illumination and laser speckle correlation analysis were performed. Based on various experiments and comparisons with the theoretical Gompertz model, colony radius growth curves were obtained. It was shown that the Gompertz model can be used to describe both types of analysis. A comparison of the two methods shows that laser speckle contrast imaging, combined with signal processing, can detect colony growth earlier than standard CFU counting method under white light illumination.


Introduction
Determination of the viable microbial cells in a sample is one of the central tasks of epidemiology. Each viable cell initiates the development of one colony on an agar plate medium called colony forming units (CFU). Colonies are counted after they are clearly visible to the naked eye. In standard methods, the waiting time is 18-40 hours for CFU's to "develop" before counting them [1]. Especially, in medicine, pharmacy, veterinary, industry, food production industry, and environment monitoring the information of the actual number of viable microbial cells highly relates to the health issues of the patient or society. Knowing the actual number of viable microbial cells in a sample is crucial to getting results as early as possible. Thus, new methods allow detecting the growth of microorganisms earlier than existing methods and can significantly improve epidemiological work [2]. The development of new cost-effective methods for assessing the microbial activity to reduce detection time and labor costs is of great practical interest for scientists and technology developers. One of the options for fast and early evaluation of the activity of microorganisms' is a non-contact optical technique called -laser speckle contrast imaging. Laser speckle is an interference pattern produced by coherent light reflected or scattered from different parts of the illuminated surface. In the case of stationary, static scatters, the scattered light creates constant patterns of laser speckles. However, if scatters such as particles in a fluid are spontaneously moving (e.g., Brownian motion) the individual speckle looks like it is "twinkling" or "boiling". This phenomenon is called "time-varying speckle." Regarding this phenomenon the laser speckle imaging technique has been proved to monitor moving particles in optically inhomogeneous media by analyzing time-varying laser speckle patterns. Thereby, the analysis of laser speckles patterns provides a powerful opportunity for quantifying the movement activity at the micro and macroscale. Currently, one of the popular data processing algorithms for generated time variable laser speckle patterns is correlation methods. In cases were a rough surface is used and it is deformed, or shaken, or displaced, the corresponding offset (displacement) can be observed in the speckle image [3]. This offset can be described by the position of the peak of the cross-correlation function between frames. The offset of the autocorrelation peak (the frame with itself) is always zero. A cross-correlation peak offset (between frames) indicates that is a bias between them. The correlation coefficient can be used to analyze activity in the form of a time-varying speckle pattern [4]. Each frame of the sequence is compared with the previous frame. Thus, a change is in the correlation coefficient over time is obtained. Low temporal variation of the correlation coefficient in observed area implies to its relative inactivity in frame of sensitivity of detection method. The correlation coefficient graph as a function of the frame number (or time) represents of the activity of observed process.
In a previous paper [5], we showed how the correlation method can be used to convert the change between subsequent frames into a temporal signal. By analyzing the received time signal, it is possible to detect events caused by the vibration of the measured surface or activity on it. For example, the dynamic propagation of a bacterial colony on the solid media surface. In the current work, we will continue to develop this method. It will be used to measure the size of the bacterial colony and the growth rate.
Literature data indicate significant advances in laser speckle imaging techniques and their potential application to evaluate dynamic processes in microbiological media. Laser specklebased approaches can be used to evaluate bacterial chemotactic response in agar plates [6], and to distinguish motile bacteria from fungi [7], for example. Technology using speckle decorrelation time maps has been demonstrated for the detection of E. coli and B. cereus on meat (chicken breast) [8]. Speckle analysis has also been applied to biomass growth kinetic measurements in liquid culture [9], characterization of CFU morphology [10], determination of antibiotic susceptibility [11,12]. As well as laser speckle imaging techniques in combination with Deep Learning (DL) and Artificial Neural Networks (ANN) have demonstrated a fast system response of antibacterial susceptibility evaluation in minimum inhibitory concentration tests [13]. In general, the laser speckle imaging approach is quite simple, providing early responses from microbiological activity in comparison with methods based on turbidity estimation methods or manual colony counting. However, according to available literature, none of laser speckle-based methods have been focused on microbial growth (CFU formation) monitoring in early stages. In current work, we will prove that dynamic laser speckle image analysis methods can be used to detect and predict the CFU of different microbes in solid media.

Microbial strains and cultivation conditions
Vibrio natriegens strain DSM 759 was purchased from German Collection of Microorganisms and Cell Cultures GmbH. V. natriegens was grown in Nutrient Broth + salts (Difco Nutrient Broth, 8 g* L-1 NaCl 15 g L-1), as suggested by [14]. Bacterial culture was maintained on agar plates; single colonies were used for inoculation in 5 mL overnight culture in respective liquid media. To observe colony growth from single cell, preculture of V. natriegens was serially diluted to achieve approximately 200 -400 cells per mL, then 5 microliters were spotted on respective agarised media in standard Petri plate (diameter 9 cm) and placed to grow in room temperature at 22°C and 26°C under 635 nm laser illumination.

Laser speckle imaging system
The system was assembled for capturing macro scale images under white light and laser illumination. The optical measurement system consists of a laser source, white light source LED, 35 mm CS lens @F18, optical attenuator, a testing agar plate (with inoculated bacteria) and a CMOS camera (Fig. 1). To avoid antimicrobial effects caused by blue and green irradiation, the red laser was selected for generation of laser speckles. In subsequent experiments the laser speckles were generated by a linearly polarized 635 nm diode pumped solid state laser (output power 50 mW). To achieve optimal exposure for image capturing as well as to avoid heating effects of illuminated plate the optical attenuator was used enabling 3-5 mW/cm 2 power density of the scattered laser light on the whole agar plate surface. The diameter of the laser beam on the surface was greater than 9 cm providing even illumination of the entire standard Petri plate.
In accordance with literature available information, the illumination conditions applied in our research are optimal and do not affect microbial growth [15]. Main components of the system are presented in Fig. 1. The speckle images were captured by a CMOS camera with 30-second intervals for experiments with different durations (10-25 hours). Interval was chosen according to the location of the useful time signal region in the spectrogram (see 3.2 for details). Exposure time was set to 1 second and was chosen according to laser illumination and lens diaphragm. Parameters of optical setup including camera resolution, lens diaphragm, camera distance to Petri plate and resulting region of interest were chosen to achieve adequate spatial resolution for detecting laser speckles. According to previous research [16], the resolution of the camera should be at least 2 pixels per speckle. Diaphragm value of F18 was chosen as optimal balance between image sharpness, speckle size and required exposure. White light experiments were performed separately from the laser speckle imaging by using the same set up (Fig. 1). For these experiments, images were taken every 15 minutes during 25 hours under white LED illumination.

Description of the algorithm for converting a speckle image into a time series
In the previous study [5], we showed that a non-contact optical method based on laser speckle imaging technique, together with image processing, allows detecting microbial activity in 2.5-3 hours after inoculation. This is much earlier than the standard counting methods used to count colony forming units (CFU) [17,18]. A method for speckle image conversion into a time signal was developed and described below.
1) First, two-dimensional normalized correlation between images following each other in time is performed. This allows detecting changes in the speckle image (between subsequent frames) because of dynamic activity [3] (Eq. (1)).
Where a(x,y) and b(x,y) are two adjacent frames in a sequence,ā andb are the average values of these two frames, u and v is spatial displacement between frames a(x,y) and b(x,y) in the directions of x and y, respectively.
2) Changes that occur between successive frames are characterized by an offset in the location of the maximum correlation value (Eq. (2)).
3) The growth of a bacterial colony is a random process. Therefore, the offset between each pair of successive frames cannot be exactly equal to an integer number of pixels. Hence, the offset between successive frames does not represent the integer number of pixels. For this reason, interpolation was performed within the maximum of the correlation function [19]. This was performed separately for x-axis and y-axis. Equation (3) shows the parabolic interpolation for the x-axis.
Where a u and b u are the coefficients of the parabola.

4)
Offsets obtained between each pair of adjacent samples were accumulated (separately for x and y axis) to consider previous offsets [Eq. (4)].
Performing this procedure between each pair of consecutive frames for the entire sequence creates a "time signal" (or signal). An increase of signal values will be observed when bacterial growth occurs. Establishing a threshold or an adaptive threshold or constant false alarm rate (CFAR) -based threshold for this signal allows detecting the region and time where growth of bacteria was observed. The presented signal analysis was performed in a semi-automatic, semi-manual mode since the adaptive threshold algorithm is still under development.

Analyses of colony growth under white light illumination
Microbial growth on the agar surface and formation of colony is a self-limiting process which starts with the maximum rate, which is gradually inhibited by exhaustion of necessary nutrients, accumulation of end products of microbial metabolism. There are many mathematical models describing microbial colony growth, among them, the Gompertz model is one of the common [20,21]. The mathematical expression of the Gompertz model is presented in Eq. (5).
Where µ is specific growth rate (h −1 ), µ 0 -specific growth rate at beginning of colony formation (h −1 ), µ i -specific growth rate at infliction (or specific inhibitory rate), t 0 represents time at beginning of the colony growth and t is the actual time (h). Equation (6) describes the growth of the colony radius as a function of time.
Equation (6) shows the growth of the colony radius, where r max is the maximal radius that the colony can reach in the given environmental conditions, r 0 is the initial radius at t 0 , µ i is the specific growth rate at the inflexion point of the area curve. Over time gradual inhibition of colony growth occurs, which can be described by µ i . To use these equations to simulate growth of real CFU, µ 0 and µ i should be found.
A specific set of parameters should be found to describe microbial colony growth using the Gompertz model. It was done experimentally for each microbial species and cultivation conditions (temperature and media). Fast growing sea bacteria Vibrio natriegens [14,23] were chosen for the experiments. Bacteria were grown on salt rich, agar plates in room temperature (see the materials and methods section). First, the series of micro images were used to find the growth rate at the beginning of CFU formation (when colony growth rate is practically equal to µ 0 ). Thus, µ 0 for V. natriegens in the room temperature was determined approximately 3.875 +/-0.25 h −1 . Also, a series of CFU images under white light were taken to experimentally find the specific V. natriegens CFU inhibitory rate (µ i ). For this purpose, the growth of the V. natriegens CFU was recorded (one image in 15 min, from 0 to 20 hours or more) to estimate the growth of the colony radius under white light illumination. The diameter of each CFU was determined from images using the imageJ program. The CFU was identified from images by visual inspection (not enhancing photo). Due to the low cell concentrations, the contrast of RGB images under white light illumination was low and CFU diameters were determined not earlier than after 8 -12 h. Colony diameters were determined from the image series over time (see example of image series in Fig. 2(b)). Using Eq. (6) the µ i for V. natriegens were calculated at given temperature and media conditions. See example of obtained results and mathematical approximation in Fig. 2(a)).
Based on the experimentally obtained colony measurements, we set maximum colony radius to be 170 pixels and initial colony radius (r 0 ) 0.1 pixels (1 pixel equals 5 micrometers). When simulating µ i for V. natriegens in the room temperature for the given colony growth, the µ i was 0.11 h −1 . However, µ i is not a fixed number. This coefficient characterizes decreasing of the colony growth rate over time. The colony growth rate is dependent on many factors such as: temperature, number of surrounding colonies, and local concentration gradient of nutrients (compare Fig. 2 with Fig. 4 and Fig. 6). Usually, the µ i can vary by 20-50% among the same organism [21,22].
To extract parameters from the given experimental data set, parameter scan was used. As a criterion we used Root Mean Square Error (RMSE) to minimum Eq. (7) to find µ i and t 0 .
Where R Gompertz is the radius estimated from the Gompertz model, R measured is the radius determined experimentally, n is the number of measurement points. RMSE values can vary in each experiment as they represent a match between theoretical and experimental curves.

Analyses of colony growth by the processing of laser speckle images
For the speckle image analysis, the growth of the V. natriegens colony under laser light illumination was recorded. The time interval between subsequent frames was 30 seconds, which, according to our previous reports, corresponds to a sampling frequency of 33.3 mHz [23,24]. The frequency domain of the observed signal is up to 16.7 mHz. According to definition described in section 2.3, "signal" (or time signal) represents the result of the correlation and interpolation algorithm between each pair of consecutive speckle image frames.
Further, the scatter of the specific growth rate µ i , with the average experimental value of 0.17 h −1 (Fig. 4) was calculated. To obtain a curve representing growth of colony radius the following steps on processing of speckle images were performed: 1) The location of the colonies was manually marked and automatically divided into 20 × 20 pixel sections; 2) Converting each 20 × 20 pixel section into a time series; 3) Determination of signal rising time at low frequencies (characterization of bacterial activity); 4) Marking and determination of the times and spatial locations of detected signals (Fig. 3, the green marker). Figure 3 represents a) the signal, b) its "energy" envelope, and c) the spectrogram. A spectrogram is a representation of a signal on a time-frequency plane using short-time Fourier transform (STFT). The spectrogram shows how the spectral density was distributed over the frequencies by observing a signal indicating colony growth (Eq. (8)-(9)): Where w is the Hamming window function, and sig[n] is the signal to be transformed. Using the window w, the signal is divided into segments and performs windowing.

STFT[k,f] is essentially the Fourier transform of sig[n]
· w[n − k], a complex function representing the phase and magnitude of the signal over time and frequency. 5) By marking the growth start times of each 20 × 20 pixel square, knowing the location of each square in space and its distance from the colony center (marked manually in step 1), the colony radius was calculated as a function of time (Fig. 4). Figure 4 represents the increase in colony radius in speckle images as a function of time obtained according to the Gompertz model (Eq. (6)). Using the scanning method for several parameters (growth rate, growth start time, maximum radius of colony) it is possible to get the most optimal suitable Gompertz curve in which the Root Mean Square Error (RMSE) value will be minimal. RMSE value (see Fig. 4) shows how much the curve differs from the model. To summarize, the above-mentioned approach captures time events that characterize dynamic changes in speckle signals for all spatial sections (20 × 20 pixels each) throughout the experimental data set. Fig. 4. Vibrio natriegens colony radius obtained by speckle image experiment (red) and theoretical Gompertz curve (blue). Interestingly, first signals above threshold level from speckle imaging can be extracted as fast as less than three hours from the beginning of the cultivation.

Comparison of colony growth measurements in white light and speckle imaging experiments
The numerous experiments were performed using speckle imaging technique and images under white light illumination (see results in Fig. 5) to understand the typical signal dynamics of V. natriegens colony growth. Comparing these two techniques, it was obtained that with the speckle imaging technique it is possible to detect microbial activity earlier than using white light imaging. The colony formation on the agar media was observed 3 hours after bacterial inoculation, while the CFU growth of the colony in white light could be detected after 8-13 hours. However, there are speckle image experiments where growth was observed later than 3 hours from the beginning of the experiment (Fig. 5). All signals depicting CFU growth (obtained from speckle and white light images) demonstrate similar dynamics (the graphs of radius increase over time are parallel to each other). However, the growth signal graphs are scattered across x axes, which can be attributed to fluctuated room temperature across the experiments thus affecting growth speed and colony detection.
Detection of the colony growth (increase of the colony radius) using speckle images demonstrates that it is possible to distinguish colony development from the background earlier than using white light images.
The growth speed of microbial CFU on the agarised media depends on many factors: temperature, distance from the neighboring colonies, local concentrations of nutrients. To test the sensitivity of the laser speckle imaging method at different room temperatures, colony growth was recorded at "low" (∼22°C) and "high" (∼26°C) temperatures. It was observed that the Vibrio natriegens colony grew more slowly at low temperatures and the laser speckle method began to observe it after 9 h (Fig. 6. blue curve). But at higher temperatures bacterial colonies started to grow faster and were detected after 4 h (Fig. 6, green curve). To find the best parameter set for approximation of the experimental data, the Gompertz model was applied for the samples at "low" and "high" temperatures. Specific growth rate µ i , time when growth startst 0 , and the error between the experimental and theoretical curves (RMSE) were found. The results are depicted in Fig. 6.
From the comparison shown in Fig. 6, the Gompertz parameters for these two "extremes" are quite alike. While the start time of the growth is different, the µ i is similar. It was observed that at 26°C room temperature the growth of V. natriegens started immediately (Gompertz model start time t 0 =0), but at 22°C room temperature, bacterial growth began after a 6.4 h delay. In both cases calculated colony growth radius can be fit by the theoretical model of colony growth. This means that speckle imaging can be applied to record growth of microbial colonies in different conditions: optimal, when microbial growth starts immediately after cell inoculation, and suboptimal -when microbial growth is hampered and therefore colonies are detected later.
Notably, the resolution of radius detection underlying speckle image processing is significantly higher in comparison with analysis of images obtained under white light illumination. Thereby, the speckle image analysis enables to detect bacteria growth in smaller spatial dimensions without using optical magnification.

Summary and discussion
Although various tests are used to determine microbial cell count in the environmental, food or patient samples, there is a permanent need for new, robust tools for rapid microbial activity detection [25]. Growth and enumeration of microbial CFU on agar plates is extensively used in epidemiological tests. Typically, one must wait for at least 24 hours to detect the presence of colonies. Our results imply, that by using laser speckle imaging and analyses technique it is possible to shorten colony detection time two or more times. We explored CFU growth dynamics of rapidly (probably the fastest bacteria we can cultivate in the lab) growing bacteria V. natriegens by white light image analyses and laser speckle imaging. Obviously, there is some "critical number of dividing bacteria" to generate a meaningful signal for both methods. Previously, it has been reported that it is not possible to detect colonies smaller than 200 micrometers in diameter under white light illumination [18]. The size of the smallest colonies of V. natriegens we detected were 14-20 pixels in diameter, or approximately 70-100 micrometers in diameter. To reach V. natriegens colony of this size, it takes 8-10 hours or more. In contrast, it takes a minimum 3 hours or typically 6 hours to generate speckle signal which differs from background and is characteristic for bacterial growth. It seems that for V. natriegens CFU detection in white light experiments approximately 10 6 cells are necessary. On the other hand, approximately 10 4 V. natriegens cells are necessary for speckle imaging signals to be detected. If the microbial cell proliferates exponentially it would take approximately 13 doublings from a single cell to reach colony size detected by speckle imaging and approximately 20 doubling times to reach colony size which could be detected in white light. However, colony growth follows Gompertz kinetics, which means that growth rate decreases over time and therefore 20 doubling times will not take 1,5 times longer than 13 doubling times. Instead, it can take two times longer or more. Thus, speckle imaging offers unprecedented analytic opportunity for CFU growth detection significantly earlier than visual inspection under white light.
The presented results demonstrate high potential for development of cost-effective solutions for fast evaluation of bacterial activity in solid media. Undoubtedly, such a system should perform real time data analysis of acquired laser speckle images, including determination of signal adaptive thresholds, counting of CFU, etc. Thus, the proposed data analysis approach will enable fast detection and counting of bacteria colony forming units in future.
Undoubtedly, the bacterial colony growth rate cannot be observed in seconds due to relatively slow doubling time of bacteria cells. Accordingly, the concept of real-time analysis of bacteria growth is conditional and requires observation (data collection) for at least minutes or even several tens of minutes. On the Fig. 3 in the interval from 3.5 to 9 hours we can clearly see signal changes that describe the growth of the colony. However, the signal can vary between local minimums and maximums each few minutes caused by unwanted environmental influences. Therefore, for effective detection of microbial growth activity we propose to use 30 minutes intervals.

Conclusion
To conclude, the proposed method based on the analysis of laser speckle time series images provides an earlier response of growing bacteria in comparison with classical CFU growth detection under white light illumination. The results (growing curves) demonstrate wide distribution which can be attributed to unstable ambient temperature, which fluctuated across the experiments and therefore altered growth speed. Undoubtedly, further additional studies performed in a controlled microbiological environment are necessary.