2.1.

Blood Hgb Correlation Models Using Full Spectra Data

To identify correlations between measured reflectance spectra and blood Hgb (i.e., gold standard and definitive diagnosis), we made use of a PLSR method. PLSR has been broadly used to model relationships among observed variables and response (or outcome) variables in the fields of chemometrics, food safety, industrial processes, and system biology.^22–28 Because PLSR assumes that observed variables (i.e., predictors) for characterizing a system or a process can be represented by a small number of latent variables (also known as components), it can work effectively, in particular, for analyzing a wide spectrum of biological data. Inherently, reflectance spectra (i.e., observed variables) often have multicollinearity as hyperspectral information. Thus, only a few underlying latent variables, which are linear combinations of original observed variables, are likely to represent most of variations in the original predictors. Although PLSR is similar to principal component regression (PCR) in terms of extracting principal components, it clearly distinguishes itself from PCR by taking variations in predictors and response variables (i.e., outcome variables) into account simultaneously.^29,30 PLSR projects high-dimensional original variables (e.g., reflectance spectra) onto a lower space of latent variables. Such transformation allows us to examine the significance of individual observed variables, making it possible to eliminate insignificant variables as variable selection methods.³¹ Overall, PLSR is a distinct method for constructing a predictive model by including both predictor variables and response variables when the predictor variables are highly collinear.

In addition, the use of PLSR is beneficial in avoiding overfitting when the size of predictors is larger than the sample size, in which multivariate linear regression is often prone to overfitting.³⁰ In our previous studies,^32–34 we intensively used model-based Hgb detections that require a priori information of the absorption spectra of all possible absorbing molecules in the skin. However, in this method, all possible absorbers in tissue should be included for highly reliable Hgb quantification, which is the primary objective of this study. In this respect, PLSR provides an alternative yet efficient method for Hgb spectral analyses by incorporating other potential yet minimal spectral features for accurate and sensitive Hgb quantification. Given such suitability for spectral analyses, we applied PLSR to build a model to determine blood Hgb levels (i.e., outcome variable) from measured reflectance spectra (i.e., predictors) in our study. After the model was trained appropriately, we further evaluated the ability for predicting blood Hgb levels for new spectral reflectance data using 10-fold cross-validation.

2.2.

Full Spectral Reconstruction from RGB

Recent optical sensing technologies heavily rely on spectrometers, spectrographs, and tunable color filters, all of which significantly limit the development of simple and economical devices.^21,35,36 As the first step for realizing blood Hgb test-comparable photometric anemia detection superior to the conventional color chart methods (e.g., FAMACHA), we investigated spectral reconstruction from RGB data that are commonly acquired from conventional cameras. This approach of spectral reconstruction from RGB data could potentially offer simple instrumentation and operation, using the currently available smartphone technologies.^21,35,36 In this respect, we performed numerical experiments to test the feasibility that a blood Hgb level can be sensitively and accurately predicted using a three-color sensor-based system in a similar manner of our previous study.²¹ First, RGB signals were acquired from measured reflectance spectra data. A camera response of RGB signals were computed such that

3.1.

Experimental Setup

To acquire reflectance spectra on the third eyelid of calves, we used a commercially available fiber-optic-based probe (Ocean Optics, Inc., Dunedin, Florida) with an outer diameter of 6.35 mm (1/4 in.).^39,40 Our intention of using the relative large-diameter optical probe was to minimize spectral variations associated the pressure exerted from the probe in contact with the tissue surface.^41–45 In particular, the effect of probe contact pressure is known to be significant with small-diameter miniature probes due to mechanical indentation effects. The optical reflectance probe consisted of one central optical fiber and six surrounding fibers, which work as a collection port and illumination ports, respectively. All of the fibers had the core dimeter of $400\mu \mathrm{m}$ with a numerical aperture of 0.22 (i.e., acceptance angle of $\sim 25\mathrm{deg}$ in air), and the separation distance between the collection and illumination was $\sim 0.5\mathrm{mm}$. A tungsten-halogen lamp (Ocean Optics, Inc., Dunedin, Florida) was coupled to the illumination ports, and a spectrometer in a range of 400 to 800 nm with a spectral resolution of 2 nm (Horiba Jobin Yvon, Edison, New Jersey) was coupled to the collection port. We also removed the background light and compensated for the system spectral responses using a reflectance reference standard (Labsphere, North Sutton, New Hampshire).²¹ Figure 1(b) shows the optical system configuration for reflectance spectra data acquisition in a farm field, as shown in Fig. 1(c).

3.2.

Tissue Phantom Test

To evaluate PLSR and the spectral reconstruction method under well-controlled conditions, we conducted a series of tissue phantom studies consisting of aqueous suspensions of microspheres (i.e., scatterers) and solutions of lyophilized Hgb (i.e., absorbers) in a similar manner in our previous studies.^32,34 We first estimated the scattering properties (i.e., transport mean free path length and anisotropy factor) of the scattering media using Mie theory.⁴⁶ Polystyrene microspheres with a nominal diameter of $0.36\mu m$ (Thermo Fisher Scientific Inc., Waltham, Massachusetts) were used, resulting in a scattering pathlength of $90\mu \mathrm{m}$ and a anisotropy factor of 0.73 at $\lambda =600\mathrm{nm}$. Second, we gradually increased Hgb content by adding lyophilized Hgb (Sigma-Aldrich, St. Louis, Missouri) into the scattering suspension from 0 to $\sim 23\mathrm{mg}/\mathrm{mL}$. The optical probe was submerged in the suspension with a total volume of 21.5 mL and a height of 15.0 mm and reflectance spectra were recorded. Figure 2 shows representative spectra from the tissue phantoms as a function of Hgb content. The overall reflectance intensity for each Hgb sample decreases as Hgb content increases, while the unique Hgb spectral signatures around 420, 540, 560, and 580 nm in the visible wavelength range (i.e., Soret and Q bands) are manifested.

Fig. 2

Representative spectra of various Hgb content from a series of tissue phantoms. The overall reflectance intensity for each Hgb sample decreases as Hgb content increases, while the unique Hgb spectral signatures at the Soret and Q bands become stronger. The top spectrum does not include any Hgb.

3.3.

Pilot Animal Study: Blood Hgb Testing and Conjunctival Redness Scoring

To evaluate the feasibility of blood Hgb test-comparable optical Hgb assessments in animals, we tested a total of 56 Holstein bull calves at $\sim 4\text{months}$ of age that were located in a commercial veal calf facility in Ohio. They were pen-housed in groups of three from the time they arrived at $\sim 4$ to 6 weeks of age until they were marketed at 6 months of age. During the growing process, blood was routinely collected periodically from either all the calves or a subset of calves for CBC determination. The producers used blood Hgb values to determine whether any calves require iron supplementation. For our study, immediately before or after optical spectral measurements, we collected blood with a volume of 5 mL from the jugular vein into an evacuated ethylenediamine tetraacetic acid tube as an anticoagulant for blood collection. We made spectral measurements by lightly placing the optical probe against the third eyelid of restrained calves. We analyzed blood Hgb using a commercially available hematology system (CELL-DYN 3700, Abbott Diagnostics, Lake Forest, Illinois). Primarily, as the gold standard for definitive diagnosis, blood Hgb levels were used to correlate with spectral reflectance readings from the eyelid. For a subset of calves ($n=31$), we also obtained FAMACHA-like conjunctival redness readings in a score of 1 to 5 [pink/red to white mucous membranes in Fig. 1(a)] from two trained veterinarians and selected the lower score between two independent scores in each animal.

4.1.

Reconstruction of Reflectance Spectra from RGB

As shown in Figs. 3(a) and 3(b), the representative full spectra reconstructed from the RGB signals significantly resemble the original spectra in both phantom and bovine samples. Specifically, we estimated prediction errors between the reconstructed reflectance spectra and the original spectra. When 95% confidence intervals of mean differences (dark area) at each wavelength are shown in Fig. 4, the reconstruction error patterns (confidence intervals) in wavelength are strongly associated with the spectral sensitivities of the RGB camera sensor but not much related to the samples. For both phantom and bovine experiments, the confidence intervals at around $\lambda =400\mathrm{nm}$ and $\lambda =700\mathrm{nm}$ become wider. These limitations correspond directly to the low spectral sensitivities of the RGB camera as included on the background of Fig. 4. We also validated the reconstruction algorithm using leave-one-out cross-validation due to the relative small sample size. For the phantom study and the bovine experiment, the average $R^2$ were 0.999 and 0.985, and the average RMSE of cross-validation were 0.0024 and 0.0068, respectively. As expected, the phantom samples in the strictly controlled environment have enhanced accuracy for the spectral reconstruction than the bovine ones. The bovine result still supports the feasibility of the RGB-based reconstruction approach that a blood Hgb level can be accurately predicted using a three-color sensor-based system.

Fig. 3

(a, b) Spectra reconstructed from RGB signals in representative phantom and bovine samples, respectively. The reconstructed spectra significantly resemble the original spectra.

Fig. 4.

(a, b) Estimated prediction errors between reconstructed reflectance spectra and original spectra in phantom and bovine samples, respectively. 95% confidence intervals of mean differences (dark area) at each wavelength are depicted. The confidence intervals at around $\lambda =400\mathrm{nm}$ and $\lambda =700\mathrm{nm}$ become wider. These limitations are related to the low spectral sensitivities of the RGB camera as shown on the background (blue, green, and red curves).

4.2.

Blood Hgb Correlations with RGB

Based on the full reflectance spectra reliably reconstructed from the RGB signals above, we determined correlations between actual Hgb and estimated Hgb from the reflectance data, using PLSR. For the phantom study, the PLSR method reliably predicted actual Hgb using the reflectance spectra or the RGB data. Figures 5(a) and 5(b) show correlations between the actual and optically measured Hgb values from the full spectral data and the RGB data in the phantom study, respectively. Obviously, contributing from the reconstruction error from RGB, the $R^2$ value in Fig. 5(b) is slightly lower than that of the full spectral data. For the bovine study, the $R^2$ value of 0.857 shows the feasibility of the blood Hgb comparability using the full spectral reflectance measurements [Fig. 5(c)]. On the other hand, the correlations for both original and reconstructed reflectance spectra are reduced as shown in Figs. 5(c) and 5(d).

Fig. 5

(a, b) Correlations between actual and optically measured Hgb values from the full spectral data and the RGB data in the phantom study, respectively. Due to the reconstruction from RGB, the $R^2$ value in (b) is slightly lower than that of the full spectral data in (a). (c, d) Correlations between actual and optically measured Hgb values from the full spectral data and the RGB data in the bovine study, respectively. Compared with those of the phantom study, the correlation values for both original and reconstructed reflectance spectra are slightly reduced, due to several factors including a narrow range of blood Hgb levels in our study population.

We also report mean squared prediction errors (MSPECV) through 10-fold cross-validation for each case in Fig. 5, which is an important metric of prediction accuracy for the PLSR models. Figures 6(a) and 6(b) show changes in MSPECV as the number of components increases in the PLSR model. Initially, an increased number of components in the PLSR model contributes to better representation of variations in the observed variables (i.e., reflectance spectra) and the response variables (i.e., lab-based blood Hgb) simultaneously, thus making its prediction errors lower. As shown in the insets of Fig. 6, each component contributes to different percentage variations accounted for the response variables. However, as the number of partial least square (PLS) components increases, MSPECV reaches an optimal number of PLS components. Above these levels, the PLSR model starts overfitting, meaning that random noises in the spectral data can be involved in the model. As a result, the prediction error mostly increases again. In this aspect, we note that $R^2$ would not be an ideal metric to use for assessing its predictive ability because $R^2$ continues to grow with an increase in the number of components.

Fig. 6

(a, b) Changes in MSPECV as a function of the number of PLS components in the phantom and bovine studies, respectively. Although an increased number of components in the PLSR model results in low prediction errors, MSPECV reaches to optimal numbers of PLS components [i.e., four in (a) and 11 in (b)]. Insets: The cumulative percentage of variances in the response variable (i.e., true Hgb) as a function of the number of components.

In the PLSR model, the degree of freedom can be understood in term of the number of components, which also captures the complexity of the model and is useful for determining the final model. Basically, our Hgb correlation model using PLSR allows us to increase the degree of freedom to have a higher correlation of optical Hgb and actual Hgb. However, we cannot continue to add more components as the complexity of the model increases. Indeed, for our final models, we limited the number of components, because a higher degree of freedom adds more errors. The optimal numbers of PLS components were determined to be four and 11 in the phantom and bovine studies, respectively. The behavior of the phantom data can be explained by a simpler model, compared with the bovine data.

5.1.

Limitations of Conjunctival Redness Reading

The presented method could potentially be useful for livestock that cannot be evaluated with the FAMACHA system. While FAMACHA is well established for sheep and goats, it has not yet been validated for cattle and calves.^5,10,11 Such a conjunctival redness scoring system has limited applications in cattle and calves, although some studies found that hematocrit is linearly correlated with FAMACHA scores in calves.⁴⁷ Indeed, we found no evidence of associations of conjunctival redness scores with blood Hgb levels in our study population. The conjunctival redness scoring result from a subset of the calves shows no significant correlation with blood Hgb levels ($R^2=0.004$ with a $p$-value of 0.74), as shown in Fig. 7(a). This null result of the FAMACH-like test indicates that conjunctival redness scoring in calves may be presented in a delayed manner for clinical anemia, compared with sheep and goats. Thus, our proposed method could potentially be beneficial for anemia detection of calves and cattle. The fact that the probe was physically placed on the third eyelid required the calf to be restrained for a short period of time but was less invasive than collecting blood.

Fig. 7

(a) Association of conjunctival redness with blood Hgb levels. The conjunctival redness scoring from a subset of the calves ($n=31$) shows no significant correlation with blood Hgb levels, supporting the idea of RGB camera-based photonumeric anemia detection. (b) Blood Hgb correlation with mere RGB without spectral reconstruction in the bovine study. The result of multiple linear regression shows that mere RGB data without reconstruction do not provide sufficient information to reliably assess blood Hgb test-comparable Hgb.

5.2.

Limitations of Conventional RGB-Based Photometric Technologies

Clinical examination of pallor in conjunctiva, nailbed, tongue, and palm has been extensively studied for cost-effective and simple anemia assessments in humans.^16,19,48 Although conjunctival pallor is valuable information as a clinical sign for severe anemia, it cannot provide reliable diagnosis in clinical settings. Further, quantification of Hgb from conjunctival pallor using digital photography has received attention.^17,18 The common agreement in the medical community is that this method still lacks sensitivity and specificity for anemia diagnosis in conventional clinical settings. As a result, these previous studies strongly indicate that RGB information would not be sufficient to have reliable correlations with actual Hgb content. In our study, we also conducted multiple linear regression of blood Hgb levels (i.e., outcome variable) against RGB (i.e., predictor variables). Although the R (red) channel is associated with blood Hgb with a $p\text{-value}=0.047$, the correlation coefficient is extremely low with $R^2=0.26$ in Fig. 7(b). This regression result clearly supports the idea that detailed spectral information is mandatory for computing an absolute value of Hgb content. We note that this limitation of mere RGB information is also reflected in the conjunctival redness scoring result reported in Sec. 5.1. [Fig. 7(a)]. In this respect, the mathematical reconstruction of hyperspectral data from RGB can offer a new class of conjunctival pallor assessments for laboratory blood test-comparable anemia diagnosis.

5.3.

Partial Least Square Component Analyses

To interpret the characteristics of the PLS components, we conducted spectral analyses of PLSR for the phantom study and bovine experiments. In Fig. 8, PLS components depict how the original variables (i.e., spectral reflectance intensities at each wavelength) contribute to the formation of the PLSR model. The PLS weights of components show which predicator variables are associated with the response variable and which ones convey critical information for identifying correlations with actual Hgb and spectroscopic Hgb. Several components have the unique Hgb spectral pattern around 420, 540, 560, and 580 nm in both phantom and bovine studies, which correspond to Soret and Q bands of Hgb molecules. Compared to the phantom study [Fig. 8(a)], the PLS weights of components in the bovine study are noisy especially above 650 nm. However, the similar spectral peaks or dips around 420, 540, 560, and 580 nm still reflect the Hgb absorption signatures in the visible range. Overall, the spectral shapes of the components are in good agreement with the Hgb signatures shown in the reflectance spectra (Figs. 2 and 3).

Fig. 8

(a, b) PLS weights of representative PLS components in the phantom and bovine spectral analyses, respectively. For the phantom data, first to fourth components are selected and for the bovine data, 1st, 5th, 7th, and 11th components are selected for display. The PLS weights show how strongly each component depends on the original predictors.

5.4.

Probe Contact Pressure Issues

Although the relatively large-area probe was employed in contact with the third eyelid of calves, the probe pressure effect cannot be ruled out in our animal study, given that the immobility of the animals were not ensured during optical readings. Indeed, the influence of probe contact pressure on spectral reflectance measurements of tissue has been intensively investigated, because the exerted pressure can reduce local blood volumes.^42–45 Spectral alterations and temporal variations associated with contact pressure are a critical challenge for optical diagnosis in conjunction with endoscopy. In this respect, we are currently considering a few different noncontact configurations that can be implemented using RGB cameras or smartphones. We further expect that a camera-based FAMACH-like system will allow clinically relevant assessments of anemia, highly comparable to lab-based blood Hgb tests in cases where conjunctival redness readings are challenging.

5.5.

Limitations of Our Study

Although other studies have examined the relationship between anemia and RGB photometric information, to our knowledge this is the first to examine associations between true Hgb and reconstructed full spectra in the third eyelid of calves. However, our animal study has limitations: first, a potential pitfall for the proposed training-based approach, such as RGB-based reconstruction, and PLSR is the requirement of a wide range of training set of reflectance spectra for accurate and precise prediction of actual Hgb. As a universal limitation for any training-based approaches, this requirement can involve a proper selection of samples, which in turn affects the prediction performance of estimating true blood Hgb levels. As discussed in Sec. 4.2. Blood Hgb correlations with RGB, one possible source of the lower performance in the bovine study stems from the narrow range of blood Hgb levels only from 6 to $11\mathrm{g}/\mathrm{dL}$. The normal range of Hgb is 9 to $15\mathrm{g}/\mathrm{dL}$ in cattle and the cutoff for anemia is $7\mathrm{g}/\mathrm{dL}$ in veal calves. This means that our study population included limited cases of moderate and severe anima. In addition, the lower $R^2$ values in the animal study can be attributable to other several factors in the measurement environment, including the movement of calves during optical reading on the eyelid and the limited control of the ambient light in the farm field.