# Reagentless Vis-NIR Spectroscopy Point-of-Care for Feline Total White Blood Cell Counts

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## Abstract

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## 1. Introduction

#### 1.1. White Blood Cells and Blood Spectroscopy

#### 1.2. Data Augmentation

## 2. Methods

#### 2.1. Hemogram Analysis

#### 2.2. Spectroscopy

#### 2.3. Spectral Data Augmentation

#### 2.4. Benchmarking

- Partial least squares regression (PLS): PLS maximizes the covariance between the spectra matrix $\mathbf{X}$ and the blood hemogram matrix $\mathbf{Y}$, by determining the eigenvectors of ${\mathbf{X}}^{t}\mathbf{Y}$ [46,47]. The method forces the latent structures of spectra and hemogram ($\mathbf{t}$ and $\mathbf{u}$) to be equal (NIPALS or SVD algorithm), for the correspondent basis ${\mathbf{P}}^{t}$ and ${\mathbf{Q}}^{t}$ [46], where $\mathbf{X}=\mathbf{T}{\mathbf{P}}^{t}$ and $\mathbf{X}=\mathbf{U}{\mathbf{Q}}^{t}$. It further deflates sequential orthogonal eigenvectors of the remaining information in ${\mathbf{X}}^{t}\mathbf{Y}$. The number of latent variables (LV) is optimized by the cross-validation of the minimal predicted sum of squares. PLS uses an oblique projection to determine the ${b}_{pls}$ coefficients in $Y=X{b}_{pls}$, which, albeit it linear combination of LVs, can model spectral information non-linearities [47,48].
- Local PLS (LocPLS): breaks down the complexity of the feature space by KNN classification based on the similarity of spectral features given by the Euclidean distance between sample coordinates. An ensemble of PLS models is generated for each cluster. The dimensions of the feature space and number of the cluster was optimized by cross-validation/hold-out samples [49].
- Self-learning Artificial Intelligence (SLAI): uses a two-step approach that (a) features space optimization for providing equivalence between the spectral information ($\mathbf{T}$) and blood hemogram ($\mathbf{U}$) latent spaces; and (b) performs a local covariance mode (CovM) search for unscrambling groups of samples that have the same type of interferences, providing a direct quantification between spectra and nutrients with a single dimension (or eigenvector) exhibiting stable co-variance (${\mathbf{X}}^{t}\mathbf{Y}$) [1].

#### 2.5. Total Error and Bias Analysis

## 3. Results and Discussion

#### 3.1. WBC Blood Spectroscopy

#### 3.2. Significance and Representability

#### 3.3. WBC Quantification

#### 3.4. Bias–Variance Analysis

#### 3.5. CovMs Interpretation

#### Towards Information Specificity

- Using independent spectral information allows us to diagnose natural correlations, which are highly common in complex biological information. A natural correlation between WBCs and RBCs can lead to dataset specificity but not WBC specificity; that is, WBCs are inferred by the intrinsic correlation of WBCs and RBCs. The isolation of WBC information provides a cause–effect model, preserving both information equivalence and statistical significance;
- The isolation of independent non-dominant information minimizes interference and maximizes WBC information. In this way, the sensitivity of WBC detection and quantification is increased (e.g., 85% at 7 × ${10}^{9}$ cell/L, Figure 4c).

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ASVCP | American Society of Veterinary Clinical Pathology |

BBL | Beer–Lambert Law |

Bil | Bilirubin |

BT | Blind Testing |

CovM | Covariance Mode |

CV | Cross-validation |

EDTA | Ethylenediaminetetraacetic Acid |

Hgb | Hemoglobin |

HO | Hold out samples |

HTC | Hematocrit |

IoT | Internet of Things |

LocPLS | Local Partial Least Squares |

LV | Latent Variables |

MAPE | Mean Absolute Percentage Error |

PCV | Packed Cell Volume |

PLS | Partial Least Squares |

PLT | Platelets |

POC | Point-of-care |

R | Pearson Correlation |

RBCs | Red Blood Cells |

RI | Reference Interval |

ROI | Region of Interest |

RWD | Real World Data |

SLAI | Self-learning Artificial Intelligence |

SSD | Synthetic Spectroscopy Data |

TAE | Total Allowable Error |

TE | Total Error |

TV | Target Values |

UV-Vis | Ultraviolet–visible |

Vis-SWNIR | Visible Short-Wave Infrared |

WBCs | White Blood Cells |

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

**a**) sampling and spectroscopy procedures—venipuncture performed at the jugular (2) or cephalic (3) veins for hemogram analysis and single drop for POC spectral recording; a single drop can also be collected at the auricular vein (1). (

**b**) Data augmentation through hibridization of real-world data (RWD) into synthetic spectroscopy data (SSD), validation procedures using RWD and SSD as optimization and validation datasets to test SSD representativity of RWD and knowledgbase expansion.

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

**a**) cat blood spectra () low WBCs, () high WBC examples, and () RBC Hgb major inteference bands (539–576 nm); (

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

**c**) Cell packing, scattering and WBC absorbance effects and impact on observed spectra; (

**d**) PLS scores of blood spectra—translating maximum covariance to WBCs, where • SSD blood samples, • RWD blood samples, • low WBCs and • high WBCs and → hemogram PCA loadings and main gradient direction in PLS scores space.

**Figure 3.**WBC prediction for (

**a**) SLAI with SSD as CV optimization and RWD as HO blind test samples; (

**b**) SLAI with RWD and SSD as CV and HO samples, where (•) represent the hybridized SSD samples and (•) the RWD blood samples, respectively. Green shaded rectangle () represents the WBC reference interval for cats (5.5–19.5 × ${10}^{9}$ cells/L) and red shaded rectangle () represents the ASVCP total allowable error tolerance for high WBC diagnosis.

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

**a**) Pearson correlation coefficient for RWD and SSD, where shaded rectangles represent semi-quantitative () and quantitative () results; (

**b**) MAPE benchmarks where () represents the ASVCP TAE for WBCs (21.45%); and (

**c**) POC WBC diagnostic capacity: () percentage of correct diagnoses within WBC value interval, (

**– –**) accumulated percentage of correct diagnosis, () WBC histogram distibution; and RI for WBC () and () TAE diagnosis error tolerance.

**Figure 5.**Representative low and high CovMs: (

**a**) PLS scores space where (∘) and (∘) are low and high CovMs sample groups, • SSD blood samples, • RWD blood samples; (

**b**) spectral ROIs used for the quantification of WBCs ( low and high CovM), () and () major and minor RBC/Hgb interference bands; (

**c**,

**e**) high and low CovM sample spectra and corresponding used ROIs to quantify WBCs; (

**d**,

**f**) prediction plot for high and low CovMs.

**Table 1.**Results benchmarks for PLS, LocPLS and SLAI for real-world data, and combination of real-world data and synthetic samples data for WBC quantification in cat blood.

Real World Data (RWD) | Synthetic Sample Data (SSD) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Method | nLV | R | R^{2} | SE | MAPE (%) | p-Value | R | R^{2} | SE | MAPE (%) | p-Value |

PLS ^{(1)} | 2 | 0.1874 | 0.0350 | 5.498 | 55.45 | 0.001 | – | – | – | – | – |

PLS ^{(2)} | 15 | 0.5775 | 0.3336 | 6.109 | 44.56 | 1.12 × ${10}^{-9}$ | 0.6802 | 0.4626 | 5.135 | 65.65 | <2 × ${10}^{-16}$ |

PLS ^{(3)} | 2 | 0.1874 | 0.0350 | 5.498 | 55.45 | 0.001 | 0.2634 | 0.0691 | 9.162 | 44.60 | 0.013 |

PLS ^{(4)} | 13 | 0.5553 | 0.3084 | 7.925 | 57.31 | <2 × ${10}^{-16}$ | 0.6320 | 0.3995 | 9.736 | 34.18 | <2 × ${10}^{-16}$ |

LocPLS ^{(2)} | 5 | 0.4546 | 0.2067 | 8.576 | 58.89 | 4.16 × ${10}^{-6}$ | 0.6840 | 0.4679 | 4.480 | 31.19 | <2 × ${10}^{-16}$ |

LocPLS ^{(4)} | 7 | 0.7112 | 0.5059 | 6.673 | 46.78 | <2 × ${10}^{-16}$ | 0.6782 | 0.4599 | 9.188 | 32.16 | <2 × ${10}^{-16}$ |

SLAI ^{(2)} | 1–2 | 0.7975 | 0.6361 | 5.837 | 34.13 | <2 × ${10}^{-16}$ | 0.7369 | 0.5460 | 8.492 | 22.35 | <2 × ${10}^{-16}$ |

SLAI ^{(4)} | 1 | 0.8397 | 0.7051 | 5.192 | 32.25 | <2 × ${10}^{-16}$ | 0.7723 | 0.5965 | 7.947 | 25.86 | <2 × ${10}^{-16}$ |

^{(1)}Cross-validation optimization and hold-out metrics calculation using RWD.

^{(2)}Cross-validation optimization using SSD and hold-out metrics calculation using RWD.

^{(3)}Cross-validation optimization using RWD and hold-out metrics calculation using SSD.

^{(4)}Cross-validation optimization and hold-out metrics calculation using RWD and SSD.

**Table 2.**WBC bias analysis of WBCs in cat blood for spectroscopy POC—percentage of results in optimal, desired and acceptable categories.

Real World Data | Synthetic Sample Data | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

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

PLS _{RWD} ^{(1)} | 7.81 | 14.06 | 26.56 | 0.00 | 0.00 | 10.00 | na | na | na | na | na | na |

PLS _{SSD>RWD} ^{(2)} | 21.88 | 29.69 | 39.06 | 10.00 | 16.67 | 20.00 | 15.63 | 29.02 | 46.43 | 13.16 | 22.37 | 43.42 |

PLS _{RWD>SSD} ^{(3)} | 7.81 | 14.06 | 26.56 | 0.00 | 0.00 | 10.00 | 16.07 | 25.89 | 34.38 | 1.32 | 2.63 | 9.21 |

PLS _{SSD+RWD} ^{(4)} | 10.94 | 26.56 | 42.19 | 3.33 | 10.00 | 13.33 | 13.84 | 29.91 | 47.77 | 9.21 | 22.37 | 26.32 |

LocPLS _{SSD>RWD} ^{(2)} | 14.06 | 25.00 | 29.69 | 13.33 | 16.67 | 20.00 | 23.21 | 41.52 | 52.68 | 21.05 | 35.53 | 52.63 |

LocPLS _{RWD+SSD} ^{(4)} | 15.63 | 32.81 | 46.88 | 16.67 | 23.33 | 36.67 | 19.20 | 32.14 | 45.98 | 14.47 | 32.89 | 44.74 |

SLAI _{SSD>RWD} ^{(2)} | 20.31 | 34.38 | 50.00 | 13.33 | 30.00 | 43.33 | 23.66 | 38.39 | 54.91 | 17.11 | 26.32 | 43.42 |

SLAI _{RWD+SSD} ^{(4)} | 31.25 | 42.19 | 54.69 | 13.33 | 26.67 | 50.00 | 24.12 | 41.07 | 58.03 | 30.26 | 35.52 | 46.05 |

^{(1)}Cross-validation optimization and hold-out metrics calculation using RWD.

^{(2)}Cross-validation optimization using SSD and hold-out metrics calculation using RWD.

^{(3)}Cross-validation optimization using RWD and hold-out metrics calculation using SSD.

^{(4)}Cross-validation optimization and hold-out metrics calculation using RWD and SSD. Highlighted bold values are considered are consedered best in class.

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## Share and Cite

**MDPI and ACS Style**

Barroso, T.G.; Queirós, C.; Monteiro-Silva, F.; Santos, F.; Gregório, A.H.; Martins, R.C.
Reagentless Vis-NIR Spectroscopy Point-of-Care for Feline Total White Blood Cell Counts. *Biosensors* **2024**, *14*, 53.
https://doi.org/10.3390/bios14010053

**AMA Style**

Barroso TG, Queirós C, Monteiro-Silva F, Santos F, Gregório AH, Martins RC.
Reagentless Vis-NIR Spectroscopy Point-of-Care for Feline Total White Blood Cell Counts. *Biosensors*. 2024; 14(1):53.
https://doi.org/10.3390/bios14010053

**Chicago/Turabian Style**

Barroso, Teresa Guerra, Carla Queirós, Filipe Monteiro-Silva, Filipe Santos, António Hugo Gregório, and Rui Costa Martins.
2024. "Reagentless Vis-NIR Spectroscopy Point-of-Care for Feline Total White Blood Cell Counts" *Biosensors* 14, no. 1: 53.
https://doi.org/10.3390/bios14010053