Research Article| Volume 27, ISSUE 6, P361-367, December 2022

# Systematic evaluation of isolation processes of microorganisms using spatial statistics

Open AccessPublished:September 18, 2022

## Abstract

The evaluation of inoculation processes of microorganisms by robotic systems as well as by lab-technicians is compensable and can be missing consistency as human judgment will depend on the individual and may therefore be biased and less effective than models and algorithms evaluating spatial patterns. To address this problem, nearest neighbor analysis was used to investigate if it could be utilized as a method to evaluate isolation processes. The nearest neighbor analysis results in a comparable numeric value on the isolation process, which can be used to assess results of different inoculation processes.
In this article, images of Petri dishes and simulated plates are used to investigate the effectiveness of nearest neighbor analysis, which is a method within spatial statistics. This analysis is applied to spatial data created by applying computer vision to localize the colonies on the plates.
When evaluating plates made with the streaking technique method, it was found to be ineffective as the dense parts of the distribution resulted in the computer vision being unable to locate all of the colonies. Therefore, the nearest neighbor analysis is not suitable to evaluate streaking plates and other methods to evaluate such plates should be developed. However, when evaluating Petri dishes where the spread plating technique had been applied, it was found that nearest neighbor analysis can be a useful way to systematically evaluate isolation processes.

## Introduction

In the microbiology industry, automation is becoming more prevalent. This can especially be observed in typical areas of diagnostics where commercial inoculation systems exist, which facilitate the whole inoculation process (e.g. systems from COPAN and BD Kiestra). These solutions have helped improve the efficiency of laboratories by cutting the costs and improving the work environment [
• Bourbeau P.P.
• Ledeboer N.A.
Automation in clinical microbiology.
,
• Culbreath K.
• Piwonka H.
• Korver J.
• Noorbakhsh M.
Benefits derived from full laboratory automation in microbiology: a tale of four laboratories.
].
However, we still lack a systematic way of evaluating the quality of the isolation processes, which are performed by these automated systems as well as manually performed plating. Usually, the evaluation is conducted by using different metrics where lab technicians can quantify the quality by counting the number of colonies that can be isolated [
• Choi Q.
• Kim H.J.
• Kim J.W.
• Kwon G.C.
• Koo S.H.
Manual versus automated streaking system in clinical microbiology laboratory: performance evaluation of Previ Isola for blood culture and body fluid samples.
,
• Cheng C.W.R.
• Ong C.H.
• Chan D.S.G.
Impact of BD Kiestra InoqulA streaking patterns on colony isolation and turnaround time of Methicillin-resistant Staphylococcus aureus and Carbapenem-resistant Enterobacterale surveillance samples.
,
• Croxatto A.
• Dijkstra K.
• Prod'hom G.
• Greub G.
Comparison of inoculation with the InoqulA and WASP automated systems with manual inoculation.
,
• Iversen J.
• Stendal G.
• Gerdes C.M.
• Meyer C.H.
• Andersen C.Ø.
• Frimodt-Møller N.
Comparative evaluation of inoculation of urine samples with the Copan WASP and BD Kiestra InoqulA instruments.
]. This metric is very subjective as it depends on the concentration of microorganisms in the suspension as well as the definition of a discrete colony [
• Yue P.
• Zhou M.
• Zhang L.
• Yang Q.
• Song H.
• Xu Z.
• Zhang G.
• Xie X.
• Xu Y.
Clinical performance of BD Kiestra InoqulA automated system in a Chinese tertiary hospital.
]. More recently, an approach utilizing computer vision to assess the quality of the inoculation process has been developed. This method, however, uses computer vision and an LDA-classifier trained on a lab technicians’ definition of discrete colonies and therefore has the same risk of biases as the subjective methods [
• Croxatto A.
• Dijkstra K.
• Prod'hom G.
• Greub G.
Comparison of inoculation with the InoqulA and WASP automated systems with manual inoculation.
]. This kind of testing is dependent on having the same concentration of microorganisms on a plate to be fairly compared, which can prolong and complicate the process of evaluation.
In this article, an objective metric to evaluate the quality of manual and automated isolation processes will be presented. The human variation in evaluating is reduced with this method, and it ensures a more consistent and objective measurement. The measurements consist of R-values, which describe the distribution of particles on the plate, and is derived from nearest neighbor statistics, an offset value, which shows the mean distance from the center and the number of isolatable colonies that we define as 1mm to the nearest colony, which makes it possible to compare different plating patterns.
The presented method and its applicability will be demonstrated by using it to evaluate Petri dishes from Hvidovre Hospital (provided by Lars Karsten) and images from Vulin, Clément (2020) [

Vulin, C. Data_ColTapp. https://doi.org/10.6084/M9.FIGSHARE.12951152.V1.

]. The results obtained from these Petri dishes will be analyzed using nearest neighbor analysis, and the method will hereafter be discussed to get an understanding of the limits and application area of this subsection of spatial statistics. The discussion will compare the results with simulations, which demonstrate the differences and similarities between theory and practice.

## Spatial statistics

Spatial statistics is often applied in economics, health science, and many other fields to get an understanding of distribution patterns [
• Illian J.
• Penttinen A.
• Stoyan H.
• Stoyan D.
Statistical analysis and modelling of spatial point patterns: Illian/statistical analysis and modelling of spatial point patterns.
,
• Greenaway-McGrevy R.
• Sorensen K.
A spatial model averaging approach to measuring house prices.
]. Based on spatial statistics, we propose a metric, which makes it easy to evaluate the distribution of microorganisms in a Petri dish and thereby indirectly the quality of the inoculation process. This adds the possibility of comparing different processes and potentially allows for the optimization of a process using machine learning. Moreover, using spatial statistics decreases the level of human biases within the evaluation of plating procedures and how well these distribute the Colony-Forming Units (CFU's).
By looking at the distribution of CFU's in two dimensions, we can obtain information, which can describe the process that has placed the colonies in their specific location. This can, for example be applied to determine if we randomly distribute colonies on the surface of growth media by observing the distribution and comparing it to a simulated random distribution of points in the same space. This was first done by Clark and Evans who looked at the distribution of three species of grass in an area in 1954 [
• Clark P.J.
• Evans F.C.
Distance to nearest neighbor as a measure of spatial relationships in populations.
,
• Rogerson P.A.
Spatial statistical methods for geography.
].

### Colony-forming units in streaking and plating

There are multiple ways to distribute CFU's on a Petri dish. In this paper, we primarily focus on the plating and streaking procedures.
The streaking procedure is when the diluting is done on the plate by “streaking” the colonies from a starting point (typically on the edge of the Petri dish) [
• Sanders E.R.
Aseptic laboratory techniques: plating methods.
]. The goal is not to have an even distribution, but to have as many isolatable CFUs as possible. It will optimally result in a Petri dish where there are several indistinctive colonies at the starting point and then the dilution will decrease on the rest of the plate (as observed on the last Petri dish in the result section), making it easier to isolate the CFUs. This procedure is often used to identify the number of pathogenic microorganisms from an unknown concentration of microorganisms [
• Sanders E.R.
Aseptic laboratory techniques: plating methods.
].
The plating procedure is often conducted in two steps. The first step is making the dilution series and the second step is plating the selected dilutions onto Petri dishes [
• Sanders E.R.
Aseptic laboratory techniques: plating methods.
]. The main objective of the plating procedure is to get a distribution with the most isolatable CFU's, which would be a uniform distribution. A uniform distribution will be very unlikely and due to this a CSR [
• Illian J.
• Penttinen A.
• Stoyan H.
• Stoyan D.
Statistical analysis and modelling of spatial point patterns: Illian/statistical analysis and modelling of spatial point patterns.
]-distribution will be a more obtainable goal. When using the spread plating technique there can be multiple objectives such as screening and enrichment. As previously described, in this article the objective is to distribute the colonies on the plate in a pattern that makes them easy to count and isolate. While a uniform pattern is the most efficient, in this article it is hypothesized that randomly distributed (CSR) colonies will be the most probable outcome [
• Sanders E.R.
Aseptic laboratory techniques: plating methods.
].
There are multiple factors that can determine if the plating has been successful. When plating, we want the colony forming units to be as far from each other as possible, so it is easy to isolate and count the colonies.
The different automated inoculations systems have multiple patterns and ways to perform plating [
• Cheng C.W.R.
• Ong C.H.
• Chan D.S.G.
Impact of BD Kiestra InoqulA streaking patterns on colony isolation and turnaround time of Methicillin-resistant Staphylococcus aureus and Carbapenem-resistant Enterobacterale surveillance samples.
,
• Croxatto A.
• Dijkstra K.
• Prod'hom G.
• Greub G.
Comparison of inoculation with the InoqulA and WASP automated systems with manual inoculation.
], (for example WASP uses an inoculation loop and KD-Kiestra uses a bead) similar to manual plating, which can be performed with different techniques resulting in different patterns and those patterns can have different purposes, such as spreading the microorganisms out on the plate with the goal of the most isolatable CFUs or making areas on the plate that contain different concentrations of CFU. If the goal is to have different areas with different concentrations, it will be difficult to use the method presented to evaluate the efficiency, as the used method assumes the goal is to have a CSR-distribution (this will be further discussed in the discussion section).

### Point pattern distribution

Point patterns can either be described as clustered, random (Complete Spatial Randomness
(CRS)) or uniform. A uniform distribution is ideal as this provides the largest distance between all colonies after distribution as possible when using spread-plate technique [
• Sanders E.R.
Aseptic laboratory techniques: plating methods.
], whereas a clustered distribution pattern will make it difficult to isolate colonies due to these overlapping each other and ending up as a mixed culture. However, the hypothesis in this article is that a uniform distribution is unachievable and therefore, the optimal pattern in this scenario is the random pattern (CSR).
To get an estimate of the quality of the distribution, the distances between the colonies on the agar plates will be compared to a random (CSR) distribution. This comparison is conducted by calculating the average Euclidian distances between all colonies and their nearest neighbor (NND: Nearest Neighbor Distance) on the agar plates, and comparing this to the calculated average Euclidian distances between 300 randomly generated points and their nearest neighbors of 10.000 simulations. The comparison will result in a ratio (R) [
• Rogerson P.A.
Spatial statistical methods for geography.
]:
$R=NND¯NND¯R$
(1)

The ratio will indicate if the distributions of colony forming units are more dispersed than our randomly generated points [
• Clark P.J.
• Evans F.C.
Distance to nearest neighbor as a measure of spatial relationships in populations.
].
As described, the observed point patterns will be tested against a complete spatial random (CSR) pattern. If the pattern of the colonies resolves in an average lower distance to its nearest neighbor colony than expected from the CSR pattern, it is considered clustered. If the average is larger than expected from the CSR pattern the pattern is considered uniform, and if the ratio is 1, the distribution is considered perfectly random. It should be noted that analyzing a spatial pattern using nearest neighbor analytics can in some cases give a misleading result. This is due to the fact that since the nearest neighbor analytics only consider the nearest neighbor, instances, where neighbors are placed in pairs will provide results, which indicate the sample is highly clustered despite the possibility that the pairs are still dispersed all over the entire plate. This is expected not to be a significant problem and therefore a NND-analysis is utilized.
The methodological choice of using the NND instead of alternatives as the quadrat analysis or Ripley's K function is due to the goal which is to create a data set that is easy to compare where a NND-analysis is more powerful than the quadrat method [

Boots, B. N.; Getls, A. (1988). Point pattern analysis. reprint. Edited by Grant Ian Thrall. WVU research repository, 2020. 75.

]. On the other hand, using Ripley's k-function could unnecessarily overcomplicate the problem by using a function instead of a numeric value
To take the problem further Ripley's K function could be used to investigate the dispersion in more depth. Ripley's K function is often applied as it does not review the nearest neighbor but reviews the k-nearest neighbors
• Illian J.
• Penttinen A.
• Stoyan H.
• Stoyan D.
Statistical analysis and modelling of spatial point patterns: Illian/statistical analysis and modelling of spatial point patterns.
. If the goal is to interpret which dynamics results in how the colonies are placed the use of Ripley's K-function would make sense and would be an interesting research area.
. An example of Ripley's K-function on one distribution can be seen in the result section to demonstrate why it could be useful.
A theoretical value of $NND¯R$ can be calculated by the following equation:
$r¯E=12ρ$
(2)

Where $r¯E$ is the theorized expected mean distance to nearest neighbor for a CSR-process in an infinitely large distribution of density $ρ$ [
• Clark P.J.
• Evans F.C.
Distance to nearest neighbor as a measure of spatial relationships in populations.
].
This theoretical value should be close to equal to the simulated value of $NNDR¯$. We do not have an infinite large area therefore random points are simulated and used to calculate $NNDR¯$ instead of using the theorized value. Using simulated points also ensures the possibility to use different shapes of the inoculation plate.
The maximum R-value of 2,149 represents a uniform distribution derived from a hexagonal pattern, which maximizes the distance between the points in an infinite space Figure 1 [
• Clark P.J.
• Evans F.C.
Distance to nearest neighbor as a measure of spatial relationships in populations.
].

### Statistical significance

To determine whether the average nearest neighbor ratio is statistical significant, the z-value will be calculated. It's assumed that when the sample size is large enough the dispersion of colonies will approximately follow a normal distribution which makes it
It's assumed that the z-value can be used when the sample size is large enough which makes it meaningful to use the z-score to determine statistical significance. The z-value is calculated by the following formula [
• Rogerson P.A.
Spatial statistical methods for geography.
]:
$z=NND¯−NND¯R0.0683n2A$
(3)

Where NND is the raw mean nearest neighbor distance. NNDR is the expected nearest neighbor distance, if random. n is the number of points, and A is the sample area. The constant 0.26136 is derived from the variance when analyzing the density on a circle using a Poisson distribution [
• Clark P.J.
• Evans F.C.
Generalization of a nearest neighbor measure of dispersion for use in K dimensions.
].
The calculation is done based on the assumption that the points are free to be placed everywhere on the sample area.
The null hypothesis is given by:
$H0:NND¯=NND¯R$
(4)

The null hypothesis describes that the measured mean of the nearest neighbor distances is equal to the value of the expected nearest neighbor distance, if random. Working with a 95%-confidence level, the z-value must be between -1,96<z<1,96. If the z-value is not between this confidence interval, the null hypothesis will be rejected, which would mean that the placement of the points is either dispersed or clustered.

### Offset and isolatable CFUs

The offset value is calculated to determine if the plating is skewed to one side and therefore, can be corrected by changing the starting point of the inoculation process []. This is relevant since the starting point of an inoculation process contains the largest number of microorganisms and therefore can influence the distribution of microorganisms.
We can also determine the number of isolatable colonies by measuring, which colonies meets the requirement of a specific minimum distance to their nearest neighbor.

## Materials and methods

This section will evaluate simulations to demonstrate the possibilities and limits of the statistic method. This will describe the theoretical properties of spatial statistics used on point pattern distributions as the underlying dynamics of the simulation are known, meaning it can demonstrate, which properties that the different distributions contain.
Images from a clinical setting (Hvidovre Hospital) will be evaluated by using computer vision and spatial statistics specifying point patterns. By using the results from a clinical setting, it is possible to evaluate if the method can be used to analyze such results in practice. The results from the clinical setting will be compared to the simulated results, which are used to characterize the distribution.

### Utilization of point pattern analysis on simulated Petri dishes

This section will simulate different point patterns that will be utilized in the evaluation of the plates from clinical settings by using simulations.
The simulations provide results that can be considered objective and consistent compared to the biases that can occur with human judgment.
In the simulations, the expected results are already known as the distribution is predetermined. This property makes it possible to demonstrate, which values are characterizing different distributions and can therefore be utilized to optimize the distribution objectively. Using simulations limits the number of variables, which makes it easier to evaluate the different distributions.
The utilized simulations were developed using various formulas and generated in Python.
The simulations are represented by the blue points in Fig. 2. The distribution of the blue points has then been evaluated with nearest neighbor statistics.
To characterize the simulated plates statistically, the R and z-value as determined in the spatial statistics section have been calculated. The R-value will indicate how well the particles are distributed and the z-value will tell if the distribution is within the confidence level. A %-offset value is calculated by the following formula:
$%−offset=distancefromcenterr·100%$
(5)

The %-offset shows how far from the mean center the center of the Petri dish is.
The number of particles with a minimum distance to the nearest neighbor that is greater than 1 mm (called Isolatable CFU) [
• Croxatto A.
• Dijkstra K.
• Prod'hom G.
• Greub G.
Comparison of inoculation with the InoqulA and WASP automated systems with manual inoculation.
] is also shown. This number have traditionally been used to compare the quality of the plating.
2a: A CSR-distribution will have an R-value close to 1 and the mean center will be close to the center of the Petri dish. A simulation of a CSR-distributed Petri dish can be seen in the figure which has been generated by a random Poisson distribution (CSR). The simulation has an R-value of 1.038, which indicates it is close to a CSR-distribution. The z-value of -1.16 shows that this simulation is inside the confidence level of a gaussian distribution and therefore this kind of distribution is predicted to be the most likely.
2b: Theoretically, a perfectly uniform distribution will be optimal as it contains the most isolatable colonies. In a perfectly uniform distribution, the R-value will be close to 2.149 and the mean center will be in the center. The simulation is generated by using a hexagonal pattern. The R-value is not too close to the expected theoretical value due to the assumption of infinite space on the xy-plan when calculating the theoretical value, whereas the simulation is attempting to replicate a Petri dish where colonies do not grow close to the edge. A perfectly uniform distribution will result in the largest number of colonies that can be isolated (assuming the density is not too great). This distribution is very unlikely as it can be seen by the z-value of 33.97 that it will be outside the 95%-confidence interval in a gaussian distribution.
2c: A more likely example is a uniform dispersed pattern. In this pattern, it would be possible to isolate almost every colony. There is an R-value of 1.6, which indicates that there is a larger distance between a colony and its nearest neighbor than if it had been a CSR-distribution. The z-value indicates that it is unlikely to happen as it is outside the 95% confidence level of a gaussian distribution.
2d: To illustrate some of the problems that could occur in the production of agar plates using robotics, a random Poisson (CSR) distribution where the whole area of the plate has not been utilized (radius set to 80%) has been simulated. The R-value will be below 1 and close enough to 0 to show that the distribution is significant clustered as the z-value will be –6.74, which also means that it is outside the 95% confidence level. Most robots will spread the solution from a specific starting point. The robots' distributions of particles are replicated by translating a random distribution in a specific direction.
2e: In this example, the distribution is translated to the right to replicate a starting point to the right, where the solution is spread onto the plate from this starting point. The chance of a point getting generated is quadratic to the x-value where $x0$ is at the left of the perimeter of the circle representing a chance of 0. This gives an R-value of 0.81, a z-value of -6.37, and a %-offset of 42,73%.
The R-value indicates that the distribution is clustered, and the z-value indicates it is outside the 95% confidence level.
2f: To demonstrate the limits of the statistic method that is used, a distribution, which is slightly skewed is created. The points are generated by using the x-value as the probability of the point getting generated. In this distribution, the R-value is 1.0 and z-value is –0.31, which shows the result is statistical significant. This means that despite the skewness, the statistic method used still evaluates the distribution of CFUs to be random because the average distance to the nearest neighbor is the same as the average distance on a plate with randomly distributed colonies. It should be noted, there is one less isolatable colony in comparison to 2a.

### Analysis of plates from the life-science industry

In this part, we will investigate how our statistic method can be used to evaluate the quality of the plates from real life samples and help us understand how the dispersion of cells on the plates can be optimized. This will be done by using pictures of agar-plates from external sources. The use of external sources helps determine the limitations, best use cases of the method, and the different variables such as lighting, picture quality, size of Petri dishes etc., which cannot be controlled.
The analysis of the plates will indicate whether the method can be used for different streaking and spread plating methods, or if the different ways of the distributions of the dilutions are problematic.

### Preparation of images

The images were prepared by first cutting out the border of the Petri dish so only the agar is visible by using Hough's circle transformation (Figure 3) .
To determine the location of the growing colonies on the agar, the Laplacian of Gaussian method [
• van der Walt S.
• Schönberger J.L.
• Nunez-Iglesias J.
• Boulogne F.
• Warner J.D.
• Yager N.
• Gouillart E.
• Yu T.
Scikit-image: image processing in python.
] is used to locate the blobs [

OpenCV: Hough Circle Transform. https://docs.opencv.org/4.x/da/d53/tutorial_py_houghcircles.html (accessed 2021-12-09).

] appearing on the photos.
Usually blob detection works by identifying brighter spots (colonies) on a darker background (agar), but if the colonies are darker than the growth medium the colors are inverted. Then blob detection is applied to images (see footnote for parameter values
The following parameter values have been used for the blob detection: Petri dish 1: min_sigma=3, max_sigma=10, num_sigma=10, Threeshold=0,11, overlap=0,95. For Petri dish 2 min_sigma=3,5 max_sigma=10, num_sigma=10, Threeshold=0,11, overlap=0,9. For Petri dish 3: min_sigma=1, max_sigma=10, num_sigma=10, Threeshold=0,05, overlap=0,1. For Petri dish 4: min_sigma=8, max_sigma=10, num_sigma=10, Threeshold=0,11, overlap=0,9.
).
This can be done since the organisms used in this article makes circular colonies and therefore can be observed as blobs. The center of the blob is then used as a coordinate, which can be utilized in the spatial statistic. This way of locating CFU has the disadvantages that any overlapping colonies will possibly be detected as one single unit, and spots of light in the photos can also be detected as a colony. The images were inspected with these errors in mind.

## Results

Petri dish 1 and 2 are both outcomes of a plating process. Petri dish 1 has an R-value of 0,96, which indicates that the process is an outcome of a CSR process. However, the result is not statistical significant. There is a fairly high concentration of CFU, but it would still be possible to perform isolation of 128 colonies. The R-value of Petri dish 2 indicates that the dispersion of the colonies is going towards uniformity. The number of colonies on the plate is significantly lower compared to Petri dish 1. Due to this, a higher number of isolatable colonies was detected on Petri dish 1. This also means that a higher number of colonies can effectively be isolated.
Petri dish 3 and 4 is the result of a classical streaking technique where most of the colonies are growing near one side of the plate and then get diluted towards the other side of the plate. The most useful number in this instance is the isolatable colonies. This is due to the fact that colony detecting software is unable to accurately analyze high-density areas such as the starting points on those two plates.

### Ripleys K-function

Fig. 5 shows two examples of Ripley's K-function where the first is made for Petri dish 2 and the second is made for Petri dish 4. The first graph illustrates that the distribution of colonies on petri dish 2 is close to be following a CSR process. The second graph is made for Petri dish 4 which shows that the distribution of colonies is clustered.

## Discussion of method

It can be discussed if nearest neighbor distance statistics is the best tool for evaluating all plates. The preliminary data shows that one of the limiting factors of how well spatial statistics can be applied to evaluate plates is dependent on how well the software detecting the colonies is performing. It is also dependent on whether the colonies are visible or not. This is not only a problem caused by the software used to make the statistics but is also a source of error for the human eye. It can be argued that a certain software will be more objective than a lab-technician and in cases where the software can have problems detecting colonies, it is more than likely that a lab technician will have similar problems.

Colony Counting - Environmental Testing. Automata. https://automata.tech/solutions/microbiology/colony-counting/(accessed 2022-08-12).

,

Scan 1200 - HD automatic colony counter | INTERSCIENCE. https://www.interscience.com/colony-counter-scan-1200 (accessed 2022-08-12).

,
• Majchrowska S.
• Pawlowski J.
• Gula G.
• Bonus T.
• Hanas A.
• Loch A.
• Pawlak A.
• Roszkowiak J.
• Golan T.
• Drulis-Kawa Z
AGAR a Microbial Colony Dataset for Deep Learning Detection.

### Statistics

In this paper there is used two different approaches to analyze point patterns: Nearest neighbor analysis and Ripley's K-function. Nearest neighbor analysis only observes the distance between a colony and its nearest neighbor while Ripley's k-function uses the relations between all colonies.
In this paper the two different approaches indicate the same dynamics of the distribution and Ripley's K-function does not contribute with additional value and which is why nearest neighbor analysis is found most valuable. In general, Ripley's K-function can add value to a spatial analysis as it gives a better understanding of the underlying dynamics. In the specific case of comparing plates a numeric value (from the nearest neighbor analysis) simplifies the interpretation.

### Streaking

Streaking is often used on samples with unknown concentration and the starting point will contain numerous cells, which can result in non-distinctive colonies. When the colonies are not detected, it can affect the result of the spatial statistics as the location and the number of colonies are not known. Therefore, it can be argued that the method is not highly useful when analyzing a streaking pattern. The goal of streaking is not to obtain an even dispersion of the colonies because the concentration of cells in the suspension is so high, that an even dispersion would result in problems isolating colonies on the plates because the distance between the colonies would be too small. Nearest neighbor looks at the dispersion of the colonies and therefore is not very useful in this context.
Another method to evaluate plates that have been performed streaking on could be to analyze the density of the colonies on different subsections of the plate and observe how many percentages of the plate have the optimal density of colonies. This analysis of the density could propose new streaking patterns that can optimized on different samples and swaps by combining density analysis and spatial statistics.

### Plating

When performing plating it is often done on multiple dilutions of samples containing microorganisms. This is done to ensure that one of the plates has a satisfactory number of colonies. In this article it's hypothesized that our plating process will result in a CSR-pattern. The software will be beneficial when analyzing plating patterns as the density will be in acceptable range this makes it possible for our software to detect the colonies and determine the number of colonies and because of that nearest neighbor statistics can be applied to help understand the distribution of the colonies and the quality of the plating. It can be argued that nearest neighbor statistics is a solid method to assess how effectively a spreading task has been performed and can be useful to optimize spreading techniques. Additionally, the nearest neighbor method is not dependent on knowing the concentration of microorganisms in the inoculate as the focus is solely on the placement of the colonies. That means that it should not be necessary to run specific experiments to evaluate how well a spread plating technique performs but images of plates from other experiment can be used to evaluate systems and techniques.

## Conclusion

The statistical method presented in this article is found to be a valuable asset in describing the quality of a spread plating routine, as the results for these kinds of plates are comparable with each other and the simulations that have been made. The results of the statistical method can be used to optimize a robot performing spread-plating such as the BD-Kiestra. When evaluating plates that have been made with the streaking technique, the case is not the same as the dense parts of the distribution makes the statistical method less useable. Lastly, the nearest neighbor analysis is not limited to comparing automated plates. It can also be utilized to evaluate manually prepared plates for potential errors or provide insights on how manually prepared plates can be improved.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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