## Abstract

## Keywords

## Introduction

## Spatial statistics

### Colony-forming units in streaking and plating

### Point pattern distribution

^{ a}

Where ${\overline{r}}_{E}$ is the theorized expected mean distance to nearest neighbor for a CSR-process in an infinitely large distribution of density $\rho $ [

### Statistical significance

Where NND is the raw mean nearest neighbor distance. NND

_{R}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 [

### Offset and isolatable CFUs

*centrography*. http://pysal.org/notebooks/notebooks/explore/pointpats/centrography.html (accessed 2022-01-11).

## Materials and methods

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

**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 ${x}_{0}$ 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%.

**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

### Preparation of images

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

^{ b}

## Results

### Ripleys K-function

## Discussion of method

*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).

### Statistics

### Streaking

### Plating

## Conclusion

## Declaration of Competing Interest

## References

- Automation in clinical microbiology.
*J Clin Microbiol.*2013; 51: 1658-1665https://doi.org/10.1128/JCM.00301-13 - Benefits derived from full laboratory automation in microbiology: a tale of four laboratories.
*J Clin Microbiol.*2021; : 59https://doi.org/10.1128/JCM.01969-20 - Manual versus automated streaking system in clinical microbiology laboratory: performance evaluation of Previ Isola for blood culture and body fluid samples.
*J Clin Lab Anal.*2018; 32: e22373 - Impact of BD Kiestra InoqulA streaking patterns on colony isolation and turnaround time of Methicillin-resistant Staphylococcus aureus and Carbapenem-resistant Enterobacterale surveillance samples.
*Clin Microbiol Infect.*2020; 26: 1201-1206https://doi.org/10.1016/j.cmi.2020.01.006 - Comparison of inoculation with the InoqulA and WASP automated systems with manual inoculation.
*J Clin Microbiol.*2015; 53: 2298-2307https://doi.org/10.1128/JCM.03076-14 - Comparative evaluation of inoculation of urine samples with the Copan WASP and BD Kiestra InoqulA instruments.
*J Clin Microbiol.*2016; 54: 328-332https://doi.org/10.1128/JCM.01718-15 - Clinical performance of BD Kiestra InoqulA automated system in a Chinese tertiary hospital.
*Infect Drug Resist.*2020; 13: 941-947https://doi.org/10.2147/IDR.S245173 Vulin, C. Data_ColTapp. https://doi.org/10.6084/M9.FIGSHARE.12951152.V1.

- Statistical analysis and modelling of spatial point patterns: Illian/statistical analysis and modelling of spatial point patterns.John Wiley & Sons, Ltd: Chichester, UK2007https://doi.org/10.1002/9780470725160
- A spatial model averaging approach to measuring house prices.
*J Spat Econom.*2021; 2: 6https://doi.org/10.1007/s43071-021-00013-4 - Distance to nearest neighbor as a measure of spatial relationships in populations.
*Ecology.*1954; 35: 445-453https://doi.org/10.2307/1931034 - Spatial statistical methods for geography.1st ed. SAGE Publishing: Thousand Oaks, 2021
- Aseptic laboratory techniques: plating methods.
*JoVE J Vis Exp.*2012; : e3064 Boots, B. N.; Getls, A. (1988). Point pattern analysis. reprint. Edited by Grant Ian Thrall. WVU research repository, 2020. 75.

- Generalization of a nearest neighbor measure of dispersion for use in K dimensions.
*Ecology.*1979; 60: 316-317https://doi.org/10.2307/1937660 *centrography*. http://pysal.org/notebooks/notebooks/explore/pointpats/centrography.html (accessed 2022-01-11).- Scikit-image: image processing in python.
*PeerJ.*2014; 2: e453https://doi.org/10.7717/peerj.453 *OpenCV: Hough Circle Transform*. https://docs.opencv.org/4.x/da/d53/tutorial_py_houghcircles.html (accessed 2021-12-09).*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).- AGAR a Microbial Colony Dataset for Deep Learning Detection.2021https://doi.org/10.21203/rs.3.rs-668667/v1 (preprint; In Review)

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