# Anomaly Identification during Polymerase Chain Reaction for Detecting SARS-CoV-2 Using Artificial Intelligence Trained from Simulated Data

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## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Principal Component Analysis

#### 2.2. The ML Model

#### 2.3. Data Simulation

_{p}is the maximum amplitude, b is the growth rate, Thd is the threshold (Thd) for determining Cq, rand is a function that returns random numbers from 0 to 1, and the Thd∗rand multiplication simulates noise (Figure 3).

_{Max}and L_PC

_{Min}are the maximum and minimum values of L_PC, respectively (see Algorithms 1 and 2). The simulated data are shown in Figure 3.

Algorithm 1 Random Function (Matlab) |

function y=aleat(x,x2) |

dang=abs(x-x2); |

dt=rand() * dang; |

if x > x2 |

y=x2+dt; |

else |

y=x+dt; |

end |

end |

Algorithm 2 Simulation Algorithm Using PC (Matlab) |

pos=zeros(1000,46); % class + |

neg=zeros(1000,46); % class – |

Aa=zeros(1000,46); % class Aa |

AaEx=PCA; % Principal component |

AaExn=zeros(20,46); |

k=1; |

while k < 21 % the # PC was 20 |

AaExn(k,:)=(AaEx(k,:)-min(AaEx(k,:)))./(max(AaEx(k,:))-min(AaEx(k,:))); |

r=1; |

while r < 51 |

one=ones(1,46); |

s=1; |

while s < 47 |

one(s)=one(s) * rand(); |

s=s+1; |

end |

Ap=aleat(140,300); |

Apl=aleat(0,100); |

Aa(50 * (k-1)+r,:)=(Ap. * AaExn(k,:))+one-Apl; |

r=r+1; |

end |

k=k+1; |

end |

i=1; |

Thd=20; |

while i < 1001 |

b=aleat(0.02,0.5); % parameter b |

Cqp=aleat(10,40); % Cq for + |

Cqn=aleat(41,100); % Cq for – |

Ap=aleat(40,2000); % parameter Ap |

j=1; |

Cmp=((log((Ap/Thd)-1))/b)+Cqp; % Cq for + |

Cmn=((log((Ap/Thd)-1))/b)+Cqn; %Cq for – |

while j < 47 |

pos(i,j)=(Ap./(1+exp(-b. * (j-Cmp))))+(6 * rand()); |

neg(i,j)=(Ap./(1+exp(-b. * (j-Cmn))))+(6 * rand()); |

j=j+1; |

end |

i=i+1; |

end |

X=[pos; neg; Aa]; |

#### 2.4. Big Data Classification

#### 2.5. Challenges of the Methodology

#### 2.5.1. Data Simulation from Random Function (DSRF)

Algorithm 3 Simulation Algorithm Using Random Function (Matlab) |

pos=zeros(1000,46); % class + |

neg=zeros(1000,46); % class – |

Aa=zeros(1000,46); % class Aa |

i=1; |

Thd=20; |

while i < 1001 |

b=aleat(0.02,0.5); % parameter b |

Cqp=aleat(10,40); % Cq for + |

Cqn=aleat(41,100); % Cq for – |

Ap=aleat(40,2000); % parameter Ap |

j=1; |

Cmp=((log((Ap/Thd)-1))/b)+Cqp; |

Cmn=((log((Ap/Thd)-1))/b)+Cqn; |

while j < 47 |

pos(i,j)=(Ap./(1+exp(-b. * (j-Cmp))))+(Thd * rand()/3); |

neg(i,j)=(Ap./(1+exp(-b. * (j-Cmn))))+(Thd * rand()/3); |

if j<5 |

Aa(i,j)= aleat(Thd,Ap); |

else |

Aa(i,j)= aleat(10 * Thd,2 * Ap); |

end |

j=j+1; |

end |

% data smoothing |

Aa(i,:)=(Aa(i,:)+((circshift(Aa(i,:)′,1)′))+((circshift(Aa(i,:)′,2)′))+((circshift(Aa(i,:)′,3)′)))./4; |

Aa(i,:)=(Aa(i,:)+((circshift(Aa(i,:)′,1)′))+((circshift(Aa(i,:)′,2)′))+((circshift(Aa(i,:)′,3)′)))./4; |

% offset referring to the initial intensity |

Aa(i,:)=Aa(i,:)-mean(Aa(i,1:4)); |

i=i+1; |

end |

Xa=[pos; neg; Aa] |

#### 2.5.2. Data Simulation from ML (DSML)

#### 2.6. Implementation of AI

## 3. Materials and Methods

#### 3.1. Clinical Specimens

#### 3.2. Nucleic Acid Extraction

#### 3.3. PCR Method

#### 3.4. ML Methods Analysis and Data Simulation

#### 3.5. Web Platform Design for the Implementation of AI

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Score plots of principal component (PC) 2 vs. PC 1 for real-time RT-PCR curves for SARS-CoV-2 diagnostics; (

**b**) real-time RT-PCR curve plot for the two groups found during principal component analysis (PCA).

**Figure 3.**(

**a**) Logistic function plot for different growth rate parameters used in the simulations and simulated real-time RT-PCR curves for a class; (

**b**) simulated real-time RT-PCR curves for classes no amplification (–) and abnormal amplification (Aa).

**Figure 4.**(

**a**) Score plots of PC 2 vs. PC 1 for real-time RT-PCR curves for the diagnosis of SARS-CoV-2 and their classification based on the S-Data-model; (

**b**) scheme of the best preprocessing combination, preprocessing sequence: N[Cf[Sn[D[F]]]].

**Figure 5.**(

**a**) The artificial intelligence (AI) classification scheme; (

**b**) implementation of AI for the first PCR kit for COVID; (

**c**) implementation of AI for the second PCR kit for COVID.

**Table 1.**Confusion matrix and evaluation criteria for the random forest classifier (RFC) model for the well-characterized portion (W-CP).

Test for 20% of W-CP | ||||||||
---|---|---|---|---|---|---|---|---|

Precision | Recall | f1-Score | Support | Accuracy | Matrix of Confusion | |||

Model | + | − | ? | |||||

+ | 0.976 | 1.000 | 0.988 | 40 | 0.972 | 40 | 0 | 0 |

− | 0.961 | 1.000 | 0.980 | 49 | 0 | 49 | 0 | |

Aa | 1.000 | 0.700 | 0.824 | 17 | 1 | 2 | 14 |

+ | − | |
---|---|---|

Cq | 10 to 40 | 40 to 60 |

b | 0.2 to 1.0 | 0.2 to 0.8 |

Ap | 40 to 1000 | 40 to 1000 |

**Table 3.**Confusion matrix and evaluation criteria for the random forest classifier (RFC) model of the S-Data-model.

Test for 20% of Simulated Data | ||||||||
---|---|---|---|---|---|---|---|---|

Precision | Recall | f1-Score | Support | Accuracy | Matrix of Confusion | |||

Model | + | − | Aa | |||||

+ | 1.000 | 0.989 | 0.995 | 93 | 0.952 | 92 | 1 | 0 |

− | 0.989 | 1.000 | 0.994 | 87 | 0 | 87 | 0 | |

Aa | 0,873 | 1.000 | 0.932 | 117 | 0 | 0 | 117 | |

Test for W-CP | ||||||||

+ | 0.915 | 0.993 | 0.953 | 152 | 0,960 | 151 | 0 | 0 |

− | 0.984 | 0.996 | 0.990 | 255 | 1 | 254 | 0 | |

Aa | 1.000 | 0.859 | 0.924 | 142 | 13 | 4 | 122 |

**Table 4.**Confusion matrix and evaluation criteria for the test using all data for SB-model_RFC and SB2-model.

Test of All Data for the SB-Model_RFC | |||||||
---|---|---|---|---|---|---|---|

Precision | Recall | f1-Score | Support | Accuracy | Matrix of Confusion | ||

Model | + | −, Aa | |||||

+ | 0.955 | 0.979 | 0.967 | 5938 | 0.972 | 5811 | 127 |

−, Aa | 0.984 | 0.967 | 0.976 | 8284 | 272 | 8012 | |

Test of—and Aa of All Data for the SB2-Model | |||||||

Precision | Recall | f1-Score | Support | Accuracy | Matrix of Confusion | ||

Model | − | Aa | |||||

− | 0.990 | 0.950 | 0.970 | 7287 | 0.948 | 6923 | 364 |

Aa | 0.718 | 0.930 | 0.810 | 997 | 70 | 927 |

DSRF | DSML | |||
---|---|---|---|---|

Methods | Accuracy | Log Loss | Accuracy | Log Loss |

KNC | 97.5 | 0.6 | 93.0 | 1.2 |

SVM | 96.6 | 0.1 | 97.4 | 0.14 |

RFC | 92.2 | 0.2 | 96.1 | 0.2 |

QDA | 85.5 | 3.9 | 94.3 | 1.3 |

LDA | 97.6 | 0.1 | 98.0 | 0.18 |

**Table 6.**Confusion matrix and evaluation criteria for the test using all data for the SB-model_ DSRF _LDA and the SD-A.

Test of All Data for SB-Model_ DSRF _LDA (Preprocessing = N[Cf[Sn[D[F]]]]) | |||||||
---|---|---|---|---|---|---|---|

Precision | Recall | f-Score | Support | Accuracy | Matrix of Confusion | ||

Model | + | −, Aa | |||||

+ | 0.970 | 0.971 | 0.971 | 5801 | 0.976 | 5635 | 166 |

−, Aa | 0.980 | 0.979 | 0.980 | 8287 | 173 | 8114 | |

Test of—and Aa of All Data for SD-A | |||||||

Precision | Recall | f-Score | Support | Accuracy | Matrix of Confusion | ||

Model | − | Aa | |||||

− | 1.000 | 1.000 | 1.000 | 7289 | 1.000 | 7289 | 0 |

Aa | 1.000 | 1.000 | 1.000 | 998 | 0 | 998 |

**Table 7.**Confusion matrix and evaluation criteria for the test using all data for the SB-model_ DSML_LDA and the SD-A.

Test of All Data for SB-Model_ DSML_LDA (Preprocessing = N[Cf[Sn[D[F]]]]) | |||||||
---|---|---|---|---|---|---|---|

Precision | Recall | f-Score | Support | Accuracy | matrix of Confusion | ||

Model | + | −, Aa | |||||

+ | 0.969 | 0.970 | 0.970 | 5790 | 0.98 | 5616 | 174 |

−, Aa | 0.979 | 0.979 | 0.979 | 8306 | 178 | 8128 | |

Test of—and Aa of All Data for SD-A | |||||||

Precision | Recall | f-Score | Support | Accuracy | Matrix of Confusion | ||

Model | − | Aa | |||||

− | 1.000 | 1.000 | 1.000 | 7289 | 1.000 | 7289 | 0 |

Aa | 1.000 | 1.000 | 1.000 | 998 | 0 | 998 |

Sample Availability: Samples of the compounds are not available from the authors. |

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## Share and Cite

**MDPI and ACS Style**

Villarreal-González, R.; Acosta-Hoyos, A.J.; Garzon-Ochoa, J.A.; Galán-Freyle, N.J.; Amar-Sepúlveda, P.; Pacheco-Londoño, L.C.
Anomaly Identification during Polymerase Chain Reaction for Detecting SARS-CoV-2 Using Artificial Intelligence Trained from Simulated Data. *Molecules* **2021**, *26*, 20.
https://doi.org/10.3390/molecules26010020

**AMA Style**

Villarreal-González R, Acosta-Hoyos AJ, Garzon-Ochoa JA, Galán-Freyle NJ, Amar-Sepúlveda P, Pacheco-Londoño LC.
Anomaly Identification during Polymerase Chain Reaction for Detecting SARS-CoV-2 Using Artificial Intelligence Trained from Simulated Data. *Molecules*. 2021; 26(1):20.
https://doi.org/10.3390/molecules26010020

**Chicago/Turabian Style**

Villarreal-González, Reynaldo, Antonio J. Acosta-Hoyos, Jaime A. Garzon-Ochoa, Nataly J. Galán-Freyle, Paola Amar-Sepúlveda, and Leonardo C. Pacheco-Londoño.
2021. "Anomaly Identification during Polymerase Chain Reaction for Detecting SARS-CoV-2 Using Artificial Intelligence Trained from Simulated Data" *Molecules* 26, no. 1: 20.
https://doi.org/10.3390/molecules26010020