Dynamic modeling of photoacoustic sensor data to classify human blood samples

Abstract

The photoacoustic effect is an attractive tool for diagnosis in several biomedical applications. Analyzing photoacoustic signals, however, is challenging to provide qualitative results in an automated way. In this work, we introduce a dynamic modeling scheme of photoacoustic sensor data to classify blood samples according to their physiological status. Thirty-five whole human blood samples were studied with a state-space model estimated by a subspace method. Furthermore, the samples are classified using the model parameters and the linear discriminant analysis algorithm. The classification performance is compared with time- and frequency-domain features and an autoregressive-moving-average model. As a result, the proposed analysis can predict five blood classes: healthy women and men, microcytic and macrocytic anemia, and leukemia. Our findings indicate that the proposed method outperforms conventional signal processing techniques to analyze photoacoustic data for medical diagnosis. Hence, the method is a promising tool in point-of-care devices to detect hematological diseases in clinical scenarios.

Keywords: Data-driven models; Dimensionality reduction; Photoacoustics; Signal processing.

Fig. 1

Experimental setup of the PA sensor setup. PC, personal computer; PD, photodiode; BS, beam splitter; PVDF, polyvinylidene fluoride sensor

Fig. 2

Modeling results of mean PA signals for five blood classes: healthy female (HF), healthy male (HM), microcytic anemia (A1), macrocytic anemia (A2), and leukemia (L). Subplot a shows the SVD results indicating an estimated model order $\widehat{n}=2$. Subplot b depicts the mean value of measurements (solid line), the uncertainty (shaded area), and the mean value of the modeled signal (dashed line). Subplot c shows the mean spectrum from measurements (solid line), the mean estimated output spectrum (dashed line), and the spectral linear fitting in the band from 1 to 20 MHz (straight line)

Fig. 3

Statistical analysis of the parameters retrieved by the state-space models describing the PA sensor data for five blood classes: healthy female (HF), healthy male (HM), microcytic anemia (A1), macrocytic anemia (A2), and leukemia (L). The estimated values are shown with dots alongside a thin horizontal line indicating the sample mean. For the parameters $\mathcal{P}\in {\mathbb{R}}^4$: a decay rate, b natural frequency, c first mode, and d second mode, the statistical significance is explained by $\ast p<0.05,\ast \ast p<0.01,\text{and}\ast \ast \ast p<0.001$

Fig. 4

Dimensionality reduction given by two linear discriminants, LD1 and LD2 for five blood classes: healthy female (HF), healthy male (HM), microcytic anemia (A1), macrocytic anemia (A2), and leukemia (L). a LDA results for time-domain features. b LDA results for frequency-domain features. c LDA results for ARMA model-based parameters. d LDA results for state-space model-based parameters. The stars are the centroids of each group and the ellipses refer to the 95% confidence

Fig. 5

Confusion matrix to test LDA classifier in twenty blood samples: healthy female (HF), healthy male (HM), microcytic anemia (A1), macrocytic anemia (A2), and leukemia (L). a LDA test for time-domain features. b LDA test for frequency-domain features. c LDA test ARMA model parameters. d LDA test for state-space model-based features

Algorithm 1

Dynamical model for blood classification.