Lactate has been identified as a key biomarker, with spikes co-occurring with high-risk medical conditions including sepsis and hypoxia. Despite its high medical value, current methods of Lactate measurement require repeated blood sampling from the patient, which is both costly and invasive, and consequently tends to be limited to intensive care units. Spectroscopy, a non-invasive light-based system, presents a cost-efective alternative to these traditional methods, which permits continuous measurement and improved patient monitoring. Through the use of machine learning, spectroscopic measurements can be used to estimate blood Lactate levels in an accessible and low-cost manner. In this study, machine learning models were trained on Near-infrared (NIR) spectroscopy data, to identify the best set-up for high-precision estimation of Lactate levels. The results of the analysis are used to determine the best path length for spectroscopic measurements. Feature selection is implemented to establish the most important wavelengths for prediction and inform on the most relevant spectral regions for the given task. Explainability is implemented to analyse feature contributions and allow inference of potentially interfering components that should be considered for further testing. The results showed that by using a random forest, R2 values of 0.9986 can be achieved. Feature selection increased predictive performance considerably with R2 values as high as 0.9996 and the implementation of explainability allowed the identification of important wavelength ranges.
Lactate has been identified as an important marker of patient health and can function as a proxy alarm
system for various severe health conditions including sepsis [
In this study, these advantages of spectroscopy are leveraged to design a machine learning system
that allows the prediction of Lactate levels through NIR spectroscopy. In previous works, machine
learning was used as a post-hoc approach for the classification of spectroscopic signals [
This literature review will first discuss the importance of Lactate as a biomarker for adult and infant health. It will then review current approaches to Lactate measurement and previous spectroscopic applications for Lactate measurement.
Lactate has been identified as a key indicator of patient health in a series of medical conditions. While
resting Lactate levels in healthy individuals vary between 1 and 2 mmol/L, increased resting levels
are indicative of a wide range of serious health complications including hypoxia, sepsis, diabetes and
toxin-related conditions [
Several new methodologies have been proposed to allow the continuous measurement of Lactate
levels. A comprehensive overview of the diferent approaches to Lactate monitoring can be found
in Lafuente et al. [
An alternative approach to the measurement of Lactate levels is through the use of spectroscopy. Here,
light signals are used to infer Lactate levels, hence providing the opportunity for continuous non-invasive
estimation based on a series of Lactate-correlates. Previous studies have employed Raman spectroscopy
for the quantification of Lactate levels [ 13, 14, 15]. Raman spectroscopy involves illuminating a sample
with a laser and analyzing the wavelength shifts in the scattered light. These shifts occur due to
interactions with molecular vibrations within the sample, providing a ”fingerprint” that can identify
specific molecular structures. However, these results are limited to in-vitro and ex-vivo measurements,
with in-vivo implementation remaining challenging. A diferent approach is through the use of NIR. NIR
is an absorption spectroscopy method which records which parts of the light are transmitted through a
sample. Two previous studies employing NIR for Lactate measurement were conducted by Budidha et al.
[
This section first describes the problem at hand and then details the datasets and the necessary preprocessing. The machine learning employed models, explainability methods and performance metrics are then introduced. For the sake of reproducibility, the code has been made available1.
The goal of this study is to identify the optimal path length measurement to use for measuring Lactate concentration using NIR spectroscopy. Path length refers to the distance light travels through the sample inside a cuvette. As light absorbance varies with the concentration of a compound, the ideal path length depends on the compound’s concentration. The relationship between absorbance and concentration is quantified by the Beer-Lambert law, where absorbance is calculated as the product of the molar absorbance of the sample, the concentration of the sample, and the path length [17]. If concentration becomes excessively large or small, the linearity of its relationship with absorbance is afected. Path length choice can rectify this, with shorter path lengths restoring linearity at higher concentrations and vice versa. The diference in the average response depending on path length can be seen in Figure 1. This demonstrates the importance of this choice, as the absorbance patterns vary considerably between path lengths. This study tests which path lengths are best suited for the estimation of Lactate at varying concentrations.
The dataset employed for this study contains the results of 1195 samples with varying concentrations of Lactate in a phosphate-bufered saline (PBS) solution, with the cuvette thickness as a variable quantifying path length. The three cuvette measures were 2 mm, 5 mm and 10 mm. Four diferent Lactate concentrations were measured at all path lengths alongside a clear PBS solution to use as a baseline reference. The four concentrations are 1.3 mmol/l, 13 mmol/l, 130 mmol/l and 1300 mmol/l. The spectra of the samples are measured across 350 wavelengths within the NIR range from 1014.08 nm to 2580.07 nm. To normalise the spectra, the baseline reflectance of the PBS solution is subtracted from all spectra to account for its absorption index. After pre-processing, the dataset is divided by path length and going forward, the respective subsets will be referred to as ’Path Length 2’, ’Path Length 5’, 1https://github.com/CianK99/Lactate-Detection and ’Path Length 10’. Undersampling is implemented to account for data imbalance with respect to path length and concentration. After undersampling, a total of 1047 samples are retained.
The machine learning models chosen for this project were Partial Least Squares (PLS), Least Absolute Shrinkage and Selection Operator (LASSO) and Random Forest (RF). Each will be described in turn below.
Partial Least Squares (PLS): PLS is a statistical method designed to model complex relationships by extracting latent structures from the data. It is particularly useful when predictors are highly collinear or when the number of predictors exceeds the number of observations, both of which are common problems with spectroscopic data. PLS creates latent variables as linear combinations of the original predictors and responses, aiming to maximise the covariance between these new variables while minimising the residual variance in the responses[18].
The basic form of the PLS model is:
X = TPT + E,
Y = UQT + F Here, X represents the matrix of predictors and Y represents the matrix of responses. The matrices T and U contain the latent scores extracted from X and Y, respectively. P and Q are matrices of loadings, which represent how the original variables relate to the latent components. E and F are residual matrices capturing the variability not explained by the model. PLS iteratively extracts latent variables from X and Y to optimise the shared variance. Once a latent component is extracted, the matrices X and Y are deflated to remove the explained variance. Finally, the response matrix Y is modelled as a linear combination of the latent variables:
Y = TC + F where C is a matrix of regression coeficients for the latent variables. PLS is particularly suited for handling high-dimensional data, small sample sizes, and datasets with multicollinear predictors. The optimisation of shared variance between predictors and responses ensures the model is both predictive and interpretable.
Least Absolute Shrinkage and Selection Operator (LASSO): LASSO regression is a type of linear regression that includes a regularisation component. LASSO regression aims to enhance the prediction performance and interpretability of the regression model by performing both variable selection and regularisation. The formula for LASSO is given by:
minimise 1 2n
n X(yi − β 0 − i=1
p X β j xij )2 + λ j=1
p X |β j | j=1 Here, the model aims to minimise the residual sum of squares subject to a penalty proportional to the absolute sum of the coeficients. The parameter λ controls the strength of the penalty; higher values lead to greater regularisation. This penalty term encourages the solution to have fewer non-zero coeficients, efectively conducting variable selection and promoting model simplicity and interpretability. This feature reduction is important as not all bands of light are needed for the detection of Lactate[19].
Random Forest (RF): RF is an ensemble model that enhances the performance of decision trees by combining multiple trees constructed from randomly selected subsets of data and features. Each tree in the forest operates independently, and their outputs are aggregated via averaging for regression and majority voting for classification to produce the final model prediction. This method improves generalisation and precision over individual decision trees and ofers robust predictions and better handling of overfitting.
The evaluation metrics used to compare models and classifiers in this project are R-squared (R2), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). For all metric evaluations, k-fold cross-validation is utilised, ensuring that every observation from the original dataset can appear in both the training and the test set. This method computes the model performance and aids in understanding model reliability and robustness across diferent subsets of data. For all the experiments in this project, 10 folds were used.
Explainable Machine Learning (xAI) is essential in medical applications to ensure transparency and trust. Previous studies have shown that implementing explainability can increase practitioner trust and decrease model bias [20]. Furthermore, with the introduction of the EU AI Act, the implementation of explainability in the medical domain is a legal requirement to ensure system auditability and consequential accountability [21].
For explainability in this study, feature importance in the RF model using the Mean Decrease in Impurity (MDI) method was computed. The RF model is chosen for further analysis due to its strong predictive performance during initial testing on the whole dataset as seen in Section 4.1. This method assesses each feature’s importance based on how much it reduces Gini impurity at each split in the decision trees. This reduction is summed across all trees and normalised to provide an overall importance score, with greater reductions in Gini Impurity leading to higher feature importance.
Reducing the feature space through feature selection yields several advantages for spectroscopic data. First, it eases explainability as the high dimensionality and multicollinearity of data are decreased after feature selection. Second, the identification of important features becomes more straightforward, allowing the identification of links to underlying tissue components. Finally, the runtime and complexity of models may improve in a reduced feature space, allowing for faster data processing and improved medical implementation of developed algorithms. In this study, feature selection was implemented based on the feature importance scores computed by the random forest. Models were pruned by iteratively removing the least important features and recalculating importance after each reduction. The method involves removing the bottom 20% of features at each iteration up until it reaches the top 20 features, and from this point, one feature is removed at a time.
To explain model prediction mechanisms and increase the auditability of the designed system, explainability is implemented through the use of SHAP. SHAP is a method for explaining the predictions of machine learning models based on concepts from cooperative game theory. It attributes the output of a model to its input features. SHAP values are additive, meaning the contributions of all features sum up to the diference between the average output and the actual prediction. This approach provides insights into how each feature influences the prediction, ofering a powerful tool for understanding complex models. In the current study, this allows the identification of interfering features and the identification of candidate components for further testing can be identified.
This section details the processes and results of this study’s modelling. It first presents the results of initial testing on the full wavelength ranges in Section 4.1. The results of the feature selection, based on the best-performing model, are presented in Section 4.2 and a novel approach to creating a general wavelength range on their basis is presented in Section 4.3. Finally, the outcomes of the explainability analysis are presented in Section 4.4.
Initial testing involved creating models on the full feature set for All Path Lengths, Path Length 2, Path Length 5 and Path Length 10. The initial prediction results of the implemented models are shown in Table 1. RF is found to perform the best on the All Path Lengths, Path Length 5 and Path Length 10 datasets, and is outperformed by LASSO and PLS in the Path Length 2 dataset.
Based on the initial testing results RF is identified as the best-performing model and selected for feature selection and additional testing. This selection is conducted on the basis of RF having the overall best performance as well as the most potential for improvement by feature selection. Feature selection is integrated into LASSO through L1 regularisation, efectively shrinking less important feature coeficients to zero, and in PLS through the calculation of latent variables. These built-in feature reductions limit the capacity of PLS and LASSO for further enhancement, as they have already optimised the feature space during training. As a result, RF holds more promise for iterative optimization and refinement and is used for all further testing in this paper.
To explore model performance in a reduced feature set, feature selection is implemented based on the RF model and following the methodology specified in Section 3. At each stage of reduction, the train and test R2, RMSE and MAE values are calculated. The set of features resulting in the highest test R2 for each path-length dataset individually was selected and is referred to as the optimum feature set. As seen in Figure 2, the R2 for the training set remains relatively high throughout the selection process, only decreasing when 3 or fewer features are maintained, which is likely a result of general overfitting in the training data. The testing R2 is found to perform best when retaining 14 features, which was chosen as the final number. The optimum number of features for Path Length 2, Path Length 5 and Path Length 10 were 12, 14, and 26 features respectively. In Figure 3 the most important features of each of the path length datasets are plotted against the average response of all the samples. It is clear from this graph that the features most predictive of each respective path length dataset are distinctive, with some minor overlap between Path Length 10 and Path Length 5 between 1300 - 1400 nm. This also displays a high degree of clustering between the most important features. This gives promise to a more specified tool being possible.
The prediction results after feature selection are shown in Table 2. Performance increases considerably in the reduced feature set. Interestingly, Path Length 5 now surpasses the performance of Path Length 10 in all metrics. It is worth acknowledging these R2 values are very high in all cases. While these highperformance values are encouraging and suggest a good fit for the data, they may be influenced by the lack of distinct Lactate levels in the dataset. This could result in an overestimation of model performance, as the model may be capturing patterns specific to the available data rather than generalising efectively to broader, more varied Lactate concentrations.
To investigate the concentrations of Lactate at which the model predicts with the least error, RMSE was computed for each concentration level. Table 3 presents the RMSE results for each concentration when using the optimal feature sets. Path Length 5 demonstrates the best performance across all concentrations, except at 1.3 mmol/l, where Path Length 10 outperforms it. It is important to note that the RMSE scores at zero concentration are poor for all path lengths. However, Lactate levels of zero are an artificial laboratory condition and do not reflect real-world scenarios, rendering this issue negligible. Additionally, while Path Length 5 performs best across the majority of the dataset, its lower performance at 1.3 mmol/l should be carefully considered, as this range is the most biologically significant for Lactate and should be prioritised in a medical context [22].
As the feature wavelengths used in the dataset are discrete and specific, a method to generalise this range for reproducibility and further experimentation was designed. By binning the wavelengths selected during feature selection, relevant sections of the spectrum can be identified and the size of the instruments needed for data collection could be reduced. The proposed approach takes the list of optimal features and defines a range around each identified feature. Preliminary testing determined that grouping wavelengths within a 15 nm window produced the best results. Any wavelengths within a 15nm window of each other were consolidated into the same range. A centre for each range was identified by computing the interpolated average of the wavelengths weighted by their feature importance. This means that if one of the edge wavelengths were most important for a defined range, the centre would be pulled closer to this important wavelength. These ranges and centres can be seen in Table 4. The new feature counts are presented alongside the new wavelength ranges.
When testing the RF model on these new feature ranges, the results presented in Table 5 are achieved. Path Length 5 and Path Length 10 perform better using the generalised range, with Path Length 2 performing marginally worse when compared to the results in Table 2. These ranges are more useful to inform the specifications of a tool than the wavelengths in the data. Using these feature ranges, the evaluation of RMSE by concentration yields a similar pattern to that observed with the optimal feature sets above. Specifically, Path Length 10 performs best at 1.3 mmol/l and Path Length 5 performs best for the others.
As Path Length 5 has been found to perform best across the majority of Lactate concentrations, it was selected for further analysis. SHAP is used to analyse the feature usage of the Path Length 5 model to investigate the individual feature contributions to the prediction of the model. SHAP visualisations allow for easy identification of where mistakes occur in the model.
SHAP Beeswarm Plot Figure 4 shows the generated SHAP beeswarm plot with the most to least important wavelengths of the model being shown from top to bottom. The x-axis shows the degree to which a feature supports a prediction, with points left of the origin decreasing the prediction and vice versa. The colour range from blue to red shows the importance of the feature with red features contributing more. Most of the features have a positive relationship with the Lactate concentration, increasing the predicted value of Lactate. One exception is 1695.05, which tends to increase the prediction when its value is low. This implies that this wavelength difers from the remaining features included in the analysis. This is in keeping with expectations as all remaining wavelengths fall within 100 nm of each other (1278.72 nm - 1371.99 nm) and are likely modelling the same interaction in the data. As such it is reasonable to assume that the relative distance of the 1695.05 nm feature leads to its contrasting efect on the prediction.
SHAP Waterfall Plot Individual instances of both correct and incorrect predictions were further analysed to understand the cause of the mispredictions identified in the stacked force plot. An example of a correct and incorrect prediction, respectively, for a 1.3 mmol/l sample can be seen in Figures 5a and 5b. Figure 5a shows the correct prediction with all features detracting from the mean prediction of 409.616mmol/1. Figure 5b shows how the feature contributions difer for an incorrect prediction. It is clear from the plot that the influential feature is 1371.99 as this is the only feature difering from Figure 5a. This is a prime example of the importance of explainability as it permits the auditing of the system and the successful identification of potentially problematic features.
(a) A SHAP waterfall plot of a correct prediction.
(b) A SHAP waterfall plot of an incorrect prediction identified from the stacked force plot.
This study aimed to inform the design of a tool to measure blood Lactate levels non-invasively using NIR spectroscopy via machine learning. Through analysis of achieved prediction results, the best choice of path length for NIR measurements was identified. Feature selection was implemented to establish the best wavelengths and a general wavelength range was computed. Finally, through explainability analysis, components interfering at given wavelengths can be identified and further testing for these compounds can be implemented accordingly. With RF, a 10 mm path length was found to perform best in the biologically relevant ranges of Lactate, whereas Path Length 5 performed best on average. Feature selection conducted based on the feature importance computed by the Random Forest model allowed for considerable improvement in algorithm performance. Explainability was implemented to audit the system and allowed the identification of important and potentially problematic features. In conclusion, this study demonstrates the ability of ML models to successfully estimate Lactate levels based on spectroscopic measurements and identify the best laboratory setup for such measurement. This contributes to the ongoing efort to establish non-invasive methods for the continuous measurements of Lactate in a hospital setting.
This work was conducted with the financial support of Science Foundation Ireland under Grant Nos. 12/RC/2289-P2 and 18/CRT/6223 which are co-funded under the European Regional Development Fund. This research was partially supported by the EU’s Horizon Digital, Industry, and Space program under grant agreement ID 101092989-DATAMITE. For the purpose of Open Access, the author has applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission. D. O’Hare, A. H. Holmes, Real-time continuous measurement of lactate through a minimally invasive microneedle patch: a phase i clinical study, BMJ Innovations 8 (2022). [12] S. A. Samaraweera, B. Gibbons, A. Gour, P. Sedgwick, Arterial versus venous lactate: a measure of sepsis in children, European Journal of Pediatrics 176 (2017) 1055–1060. [13] I. Olaetxea, E. Lopez, A. Valero, A. Seifert, Determination of physiological lactate and pH by Raman spectroscopy, in: 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2019, pp. 475–481. Journal Abbreviation: 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). [14] I. Olaetxea, A. Valero, E. Lopez, H. Lafuente, A. Izeta, I. Jaunarena, A. Seifert, Machine LearningAssisted Raman Spectroscopy for pH and Lactate Sensing in Body Fluids, Analytical Chemistry 92 (2020) 13888–13895. Publisher: American Chemical Society. [15] N. C. Shah, O. Lyandres, J. T. Walsh, M. R. Glucksberg, R. P. Van Duyne, Lactate and Sequential LactateGlucose Sensing Using Surface-Enhanced Raman Spectroscopy, Analytical Chemistry 79 (2007) 6927–6932. Publisher: American Chemical Society. [16] M. Mamouei, K. Budidha, N. Baishya, M. Qassem, P. A. Kyriacou, An empirical investigation of deviations from the Beer–Lambert law in optical estimation of lactate, Scientific Reports 11 (2021) 13734. [17] D. F. Swinehart, The Beer-Lambert Law, Journal of Chemical Education 39 (1962) 333. Publisher:
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