#
Point-of-Care Using Vis-NIR Spectroscopy for White Blood Cell Count Analysis^{ †}

^{1}

^{2}

^{3}

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^{†}

## Abstract

**:**

## 1. Introduction

#### White Blood Cells and Blood Spectroscopy

## 2. Methods

#### 2.1. Hemogram Analysis

#### 2.2. Spectroscopy

#### 2.3. Benchmarking

- Partial least squares (PLS): maximizes the covariance between the spectra $\mathbf{X}$ and blood WBC composition $\mathbf{Y}$ by determining the eigenvectors of ${\mathbf{X}}^{t}\mathbf{Y}$. This method forces the latent structures of spectra and composition (PLS scores—$\mathbf{U}$) to be equal (NIPALS algorithm) [37] for the determination of each correspondent basis ${\mathbf{U}}^{t}$ and ${\mathbf{Q}}^{t}$ [38]. It proceeds with deflation and sequential orthogonal eigenvectors of the remaining information in ${\mathbf{X}}^{t}\mathbf{Y}$ [37,39]. The number of deflations or latent variables are optimized by cross-validation/hold-out samples minimal predicted sum of squares (PRESS) [40]. PLS uses an oblique projection to determine the ${\mathbf{b}}_{pls}$ coefficients in $\mathbf{Y}={\mathbf{Xb}}_{pls}$ [37,39].
- Local PLS (LocPLS): uses KNN clustering to create local sub-groups, where local PLS models are optimized. The KNN clusters are obtained in the PCA scores space. The number of clusters and number of principal components (PC) is optimized by cross-validation/hold-out samples [41];
- Artificial neural networks (ANN): were introduced in spectroscopy as an approach to deal with non-linearity. ANN is a piece-wise linear combination of non-linear activation functions at each node (or neuron) of the network, being parameters optimized by back-propagation. Most ANNs in spectroscopy use PCA or PLS scores as input, being designated PCA-ANN and PLS-ANN [42,43]. The number of LV and ANN architecture (variables and layers) have to be optimized. In this research, we applied the most used template: (i) input layer—coordinates in the LV; (ii) hidden layer—optimized between two and three layers; and (iii) one output node—the estimation of WBC. The tangent and identity functions were used as hidden and output layer activation, respectively. ANN was regressed by back-propagation using the Levenberg–Marquardt algorithm;
- Least-squares support vector machines (LS-SVM): was introduced in spectroscopy to deal with the high non-linearity of feature spaces due to interference. SVM maps similarity between samples using the kernel function, mapping it into a new feature space, where the Gaussian radial basis function (RBF) maps the PLS scores ($\mathbf{U}$). The LS-SVM replaces the e-sensitive loss function by the square loss function to optimize the Karush–Kuhn–Tucker (KKT) linear system obtained by Lagrangian multipliers methodology [44]. At each U comprising an increasing number of LVs, the LS-SVM optimizes the RBF kernel width parameter ($\sigma $) and the regularization parameter of the KKT linear system ($\gamma $) [45]. The number of LV used to compute the kernel matrix is obtained by cross-validation/hold-out sample validation. LS-SVM was implemented using the kernlab library for R [46].

#### 2.4. Covariance Mode Search

- Feature space optimization: information about a constituent is present in the spectra in different scales and wavelengths. Selecting the correct features and transforms (e.g., singular value decomposition, Fourier or wavelets transforms) is essential to extract the information into a feature space that holds proportionality to the concentration of the constituents; and
- Covariance mode search: searching a group of samples within the feature space that belong to the same interference pattern. Such means that spectral features $\mathbf{X}$ hold the same information as composition $\mathbf{Y}$, with a stable covariance ${\mathbf{X}}^{t}\mathbf{Y}$.

#### 2.5. Validation

#### 2.6. Spectral Data Augmentation

## 3. Results and Discussion

#### 3.1. WBC Blood Spectroscopy

#### 3.2. WBC Quantification

#### 3.3. Bias-Variance Analysis

#### 3.4. CovM Interpretation

## 4. Conclusions

## Supplementary Materials

**a**) real-world samples and (

**b**) sythetic samples obtained by 638 mixture of two samples spectra.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural networks |

ASVCP | American Society for Veterinary Clinical Pathology |

Accep | Acceptable |

ATE | Allowable total error |

Bil | Billirubin |

BLL | Beer–Lambert law |

CovM | Covariance mode |

CV | Cross-validation |

Des | Desired |

EDTA | Ethylenediamine tetraacetic acid |

Hgb | Total hemoglobin |

HO | Hold-out samples |

HTC | Hematocrit |

IoT | Internet of Things |

KKT | Karush–Kuhn–Tucker |

LocPLS | Local partial least squares |

LV | Latent variable |

LS-SVM | Least-squares suppport vector machines |

MAPE | Mean average percentage error |

Opt | Optimal |

PC | Principal component |

PCA | Principal component analysis |

PCA-ANN | Principal component analysis—Artificial neural networks |

PLS | Partial least squares |

PLS-ANN | Partial least squares—Artificial neural networks |

POC | Point-of-care |

R | Pearsons correlation coefficient |

RBC | Red blood cells |

RBF | Radial basis function |

RI | Reference interval |

ROI | Region of interest |

RWD | Real-world knowledgebase dataset |

SE | Standard error |

SIM | Similarity |

SLAI | Self-learning artificial intelligence |

SSD | Synthetic spectroscopy dataset |

SVM | Support Vector Machines |

TE | Total error |

UV-Vis | Ultra-violet visible |

Vis-NIR | Visible near infrared |

WBC | White blood cells |

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**Figure 1.**Total white blood cell counts: (

**a**) current laboratory methods—automated cell counting using electric impedance or laser scattering, and manual blood smear count at the microscope by trained hematologist; and (

**b**) point-of-care approach—single blood drop spectroscopy counts using artificial intelligence (adopted from [12]).

**Figure 2.**WBC spectral information: (

**a**) dog blood spectra (▀ low WBC, ▀ high WBC and ▀ mixture spectra); (

**b**) PCA scores of hemogram counts; and (

**c**) PCA scores of blood spectra, where: • mixture of hemogram/spectra samples, • blood samples, • low WBC and • high WBC; → hemogram PCA loading.

**Figure 3.**WBC prediction for: (

**a**) SIM; (

**b**) PLS; (

**c**) LocPLS; (

**d**) PCA-ANN; (

**e**) PLS-ANN; (

**f**) LS-SVM; and (

**g**) SLAI; where (•) represent the mixture of samples and (•) blood samples, respectively. Blue shaded rectangle represents the WBC reference interval for dogs (5.6–17.8 × 10${}^{9}$ cells/L).

**Figure 4.**WBC quantification benchmarks: (

**a**) Pearson correlation coefficient; (

**b**) MAPE and (

**c**) absolute difference in R and MAPE between mixture and real samples predictions; and (

**d**) percentage of correct diagnosis as function of WBC POC prediction: ▀ mixture spectra and ▀ real samples.

**Figure 5.**WBC CovM demonstration: (

**a**) high and low WBC CovMs in PCA scores space—• mixture samples, • real samples; • CovM samples with low WBC, • CovM samples with high WBC, and → the CovM vector; (

**b**) High WBC CovM spectra and wavelength variance correlated to WBC (blue rectangle); (

**c**) Low WBC CovM spectra and wavelength variance correlated to WBC (green rectangle).

Method | Parameters | Dataset | R | SE (${10}^{9}$ Cells/L) | MAPE (%) |
---|---|---|---|---|---|

SIM | nPC = 3 | Mixture | 0.5005 | 8.16 | 35.66 |

n = 3 | Real | 0.1658 | 15.66 | 31.45 | |

PLS | LV = 6 | Mixture | 0.6109 | 6.87 | 29.66 |

Real | 0.5838 | 10.92 | 43.08 | ||

LocPLS | LV = 5 | Mixture | 0.6110 | 6.52 | 28.51 |

Real | 0.6619 | 10.10 | 40.37 | ||

PCA-ANN | LV = 3 | Mixture | 0.4197 | 8.01 | 46.85 |

(8:18:12) ${}^{\left(1\right)}$ | Real | 0.4934 | 12.39 | 45.32 | |

PLS-ANN | LV = 3 | Mixture | 0.5210 | 7.60 | 41.79 |

(18:20:15) ${}^{\left(1\right)}$ | Real | 0.6879 | 9.02 | 34.67 | |

LS-SVM | Mixture | 0.4207 | 7.80 | 32.83 | |

Real | 0.5976 | 7.50 | 53.04 | ||

SLAI | LV = 1 | Mixture | 0.8432 | 4.67 | 20.57 |

nCov = 100 | Real | 0.8789 | 6.92 | 25.37 |

^{(1)}Network hidden layer architecture; nPC—number of principal components. n—number of neighbors; nCovM—number of CovMs.

**Table 2.**Bias analysis for dog WBC using spectroscopy POC—percentage of results in optimal, desired and acceptable categories.

Real | Mixture | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Method | % Inside RI | % Outside RI | % Inside RI | % Outside RI | ||||||||

Opt | Des | Accep | Opt | Des | Accep | Opt | Des | Accep | Opt | Des | Accep | |

SIM | 13.30 | 20.00 | 30.00 | 0.00 | 14.29 | 14.29 | 16.72 | 33.77 | 40.54 | 9.75 | 26.89 | 34.14 |

PLS | 18.87 | 30.18 | 41.51 | 14.28 | 21.42 | 28.57 | 16.13 | 32.75 | 48.13 | 28.57 | 40.36 | 55.10 |

LocPLS | 24.53 | 41.51 | 47.17 | 14.25 | 28.57 | 42.85 | 16.62 | 30.52 | 48.63 | 19.38 | 36.73 | 52.34 |

ANNPCA | 14.00 | 24.00 | 36.00 | 0.00 | 5.88 | 11.76 | 15.67 | 28.85 | 45.03 | 24.24 | 34.34 | 44.44 |

ANNPLS | 10.15 | 27.27 | 41.82 | 8.33 | 16.60 | 33.30 | 17.04 | 31.82 | 45.86 | 32.35 | 39.22 | 40.25 |

LS-SVM | 4.72 | 14.24 | 23.81 | 25.00 | 25.00 | 25.00 | 19.19 | 33.83 | 44.94 | 20.00 | 30.00 | 36.60 |

SLAI | 24.53 | 41.50 | 58.49 | 21.42 | 28.57 | 42.87 | 27.36 | 50.99 | 66.92 | 29.59 | 52.04 | 72.45 |

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**MDPI and ACS Style**

Barroso, T.G.; Ribeiro, L.; Gregório, H.; Monteiro-Silva, F.; Neves dos Santos, F.; Martins, R.C.
Point-of-Care Using Vis-NIR Spectroscopy for White Blood Cell Count Analysis. *Chemosensors* **2022**, *10*, 460.
https://doi.org/10.3390/chemosensors10110460

**AMA Style**

Barroso TG, Ribeiro L, Gregório H, Monteiro-Silva F, Neves dos Santos F, Martins RC.
Point-of-Care Using Vis-NIR Spectroscopy for White Blood Cell Count Analysis. *Chemosensors*. 2022; 10(11):460.
https://doi.org/10.3390/chemosensors10110460

**Chicago/Turabian Style**

Barroso, Teresa Guerra, Lenio Ribeiro, Hugo Gregório, Filipe Monteiro-Silva, Filipe Neves dos Santos, and Rui Costa Martins.
2022. "Point-of-Care Using Vis-NIR Spectroscopy for White Blood Cell Count Analysis" *Chemosensors* 10, no. 11: 460.
https://doi.org/10.3390/chemosensors10110460