Using optoacoustic imaging for measuring the temperature dependence of Grüneisen parameter in optically absorbing solutions

Abstract

Grüneisen parameter is a key temperature-dependent physical characteristic responsible for thermoelastic efficiency of materials. We propose a new methodology for accurate measurements of temperature dependence of Grüneisen parameter in optically absorbing solutions. We use two-dimensional optoacoustic (OA) imaging to improve accuracy of measurements. Our approach eliminates contribution of local optical fluence and absorbance. To validate the proposed methodology, we studied temperature dependence of aqueous cupric sulfate solutions in the range from 22 to 4 °C. Our results for the most diluted salt perfectly matched known temperature dependence for the Grüneisen parameter of water. We also found that Grüneisen-temperature relationship for cupric sulfate exhibits linear trend with respect to the concentration. In addition to accurate measurements of Grüneisen changes with temperature, the developed technique provides a basis for future high precision OA temperature monitoring in live tissues.

Fig. 1

(a) Schematics of the experimental setup. (b) Photograph showing the optoacoustic probe (1), the light bars (2) and the tubes filled with samples (3) integrated via a rigid acrylic bracket. The ruler shown in front of the bracket is 15 cm long.

Fig. 2

(a) 20 × 20 mm² two dimensional optoacoustic image showing 4 sample tubes filled with aqueous solutions of CuSO₄⋅5H₂O: top left – 12 mM, top right and lower left – 60 mM, lower right – 120 mM. Linear grayscale palette is extended over the full dynamic range. The top pair of tubes is located 17 mm from the transducer array, the second pair – about 25 mm. Square indicates a 5 × 5 mm² area around the top left sample, which is magnified and presented on subsequent panels. Arrow indicates direction of illumination and location of the central probe element. (b-d) 2D optoacoustic images of a tube with 12 mM aqueous solution of CuSO₄⋅5H₂O. Images were acquired at temperatures indicated on each panel. Tube has an inner diameter of 0.635 mm and wall thickness of 0.051 mm. The selected ROI is a 0.4 mm diameter dashed circle. For direct visual comparison the images are shown in gray palette linearly scaled over the full dynamic range of the frame acquired at 12°C. The colorbar with the corresponding dynamic range is shown on panel (c). Data displayed on the panel (b) has full dynamic range [-0.040 ÷ 0.040] and the image colors are saturated for pixels with intensities below −0.020 and above 0.020. Data on panel (d) has full dynamic range [-0.006 ÷ 0.006] and, therefore, is mapped to the gray portion of the image palette. Speed of sound for background water bath is varied in reconstruction according to the temperature: (b) 1485 m/s; (c) 1455 m/s; (d) 1430 m/s. Top right corner insets on Panels (c) and (d) illustrate distorted images resulting from an optoacoustic reconstruction assuming constant speed of sound of 1485 m/s. Top right corner inset on Panel (b) shows a portion of the optoacoustic signal corresponding to the closest pair of tubes as it is registered by the central channel.

Fig. 3

Analysis of optoacoustic images for two 60 mM CuSO₄⋅5H₂O samples experiencing different local optical fluence and distortion of propagating optoacoustic waves. (a) Temporal profiles of the measured median optoacoustic intensity during cooling of the samples from 22 to 4°C. Temporal profile of the corresponding temperature change is depicted on the inset. (b) Optoacoustic intensity normalized to 20°C as a function of temperature.

Fig. 4

(a) Optical absorption spectra of aqueous solution of CuSO₄⋅5H₂O (60 mM) measured at different temperatures (5 top curves). Optical absorption spectra of distilled water are shown at 26°C and 58°C as the two lower profiles. All the spectra were measured with a reference to distilled water at 22°C. (b) Optical absorbance at 800 nm as a function of temperature for three concentrations of CuSO₄⋅5H₂O. The estimated extinction coefficient at 0°C is ε₀ = 9.38 ± 0.24 M⁻¹cm⁻¹, which is about 11% decrease from its value at room temperature.

Fig. 5

(a) Normalized optoacoustic intensity as a function of temperature for different concentrations of CuSO₄⋅5H₂O. Grüneisen parameter of water (Γ_H2O) was calculated for each degree and presented after normalization at T_n = 20°C. (b) Scatter plot and its linear fit for the parameter T₀ as a function of concentration estimated from the data slope (opened squares) and intercept (solid circles).

Fig. 6

Residuals of the linear regression models that were used to fit normalized optoacoustic intensity (solid squares) and normalized optoacoustic signals from channel number 96 (opened circles) showing the precision of the Grüneisen estimation using both techniques. Imaging: Residual sum of squares (RSS) – 0.3, R-Square – 0.998, adjusted R-Square – 0.996; Sensing: RSS - 11.7, R-Square – 0.924, adjusted R-Square – 0.854.