Exploration of linear and interpretable models for quantification of cell parameters via contactless short-wave infrared hyperspectral sensing

Abstract

The development of optical sensors for label-free quantification of cell parameters has numerous uses in the biomedical arena. However, using current optical probes requires the laborious collection of sufficiently large datasets that can be used to calibrate optical probe signals to true metabolite concentrations. Further, most practitioners find it difficult to confidently adapt black box chemometric models that are difficult to troubleshoot in high-stakes applications such as biopharmaceutical manufacturing. Replacing optical probes with contactless short-wave infrared (SWIR) hyperspectral cameras allows efficient collection of thousands of absorption signals in a handful of images. This high repetition allows for effective denoising of each spectrum, so interpretable linear models can quantify metabolites. To illustrate, an interpretable linear model called L-SLR is trained using small datasets obtained with a SWIR HSI camera to quantify fructose, viable cell density (VCD), glucose, and lactate. The performance of this model is also compared to other existing linear models, namely Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF). Using only 50% of the dataset for training, reasonable test performance of mean absolute error (MAE) and correlations (r²) are achieved for glucose (r² = 0.88, MAE = 37 mg/dL), lactate (r² = 0.93, MAE = 15.08 mg/dL), and VCD (r² = 0.81, MAE = 8.6 × 10⁵ cells/mL). Further, these models are also able to handle quantification of a metabolite like fructose in the presence of high background concentration of similar metabolite with almost identical chemical interactions in water like glucose. The model achieves reasonable quantification performance for large fructose level (100-1000 mg/dL) quantification (r² = 0.92, MAE = 25.1 mg/dL) and small fructose level (< 60 mg/dL) concentrations (r² = 0.85, MAE = 4.97 mg/dL) in complex media like Fetal Bovine Serum (FBS). Finally, the model provides sparse interpretable weight matrices that hint at the underlying solution changes that correlate to each cell parameter prediction.

Keywords: Contactless bio-sensor; Machine learning; Near infrared (NIR); Short wave infrared (SWIR).

Fig. 1

An overview of the contactless, label free rapid quantification system using a short-wave infrared (SWIR) hyperspectral camera. (A) Collection of dataset of hyperspectral images and corresponding labels. (B) Collection of hyperspectral images in SWIR range for (C) training an encoder and sparse linear regression model for metabolite prediction.

Fig. 2

Architecture of L-SLR. First, absorbance signal is converted to a polynomial basis (A), then masked based on weights from pretrained sparse linear regression model (C). Next, masked signal is passed into pretrained LDA model (E). LDA forms compressed latent space which is used to generate metabolite predictions via linear regression (F). Coefficients from LDA and SLR are then used to form weight matrix visuals (G). Models used in (C) and (E) are pretrained using a labeled dataset consisting of integer labels computed via Hilbert curve (B) that represent unique metabolite combinations.

Fig. 3

Correlation Visualization between ground truth fructose and fructose predicted by PLS-R (A, C) and L-SLR (B, D) for test data collected in dataset conditions 2 and 4 (A, B) and conditions 5 and 7 (C, D). r² and MAE are listed in the top left corner of each graph.

Fig. 4

Correlation Visualization between ground truth fructose and fructose predicted by PLS-R (A, C) and L-SLR (B, D) for test data collected in dataset conditions 9 and 10 (A, B) and condition 8 (C, D). r² and MAE are listed in the top left corner of each graph.

Fig. 5

Correlation visualization between ground truth VCD and VCD predicted by PLS-R (A) and L-SLR (B) respectively in spent cell media are shown for randomly selected test fold. r² and MAE are listed in the top left corner of each graph.

Fig. 6

Correlation visualization between ground truth glucose and glucose predicted by PLS-R (A) and L-SLR (B) respectively in spent cell media are shown for randomly selected test fold. r² and MAE are listed in the top left corner of each graph.

Fig. 7

Correlation visualization between ground truth lactate and lactate predicted by PLS-R (A) and L-SLR (B) respectively in spent cell media are shown for randomly selected test fold. r² and MAE are listed in the top left corner of each graph.

Fig. 8

Cumulative sum weight matrices produced by L-SLR (A–D) and PLS-R (E–H) for bands and cross terms across all models evaluated for fructose quantification via datasets 9–11 (A, E), dataset 8 (B, F), datasets 2–4 (C, G) and datasets 5–7 (D, H). All weights are normalized by the respective maximum of each cumulative matrix to facilitate comparison of weight matrices across models and datasets alike.

Fig. 9

Cumulative sum weight matrices produced by L-SLR (A–C) and PLS-R (D–F) for bands and cross terms across all models evaluated for quantification of VCD (A, D), glucose (B, E), and lactate (C, F) in spent cell media. All weights are normalized by the respective maximum of each cumulative matrix to facilitate comparison of weight matrices across models and datasets alike.