Mr. Ujjal K. Mandal Profile

Ujjal K. Mandal

at IIITA

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Proceedings Article | 11 August 2023 Paper

On the Born series methods for solving inhomogeneous Helmholtz equation in biomedical photoacoustics

Ujjal Mandal, Jagpreet Singh, Ratan Saha

Proceedings Volume 12631, 126310W (2023) https://doi.org/10.1117/12.2670935

KEYWORDS: Photoacoustic spectroscopy, Inhomogeneities, Biomedical optics, MATLAB, Wave equations, Tissues, Parallel computing, Fourier transforms

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The Born series methods, namely, Traditional Born Series (TBS) and Convergent Born Series (CBS), have been recently implemented to numerically solve the time-independent Photoacoustic (PA) wave equation for an acoustically inhomogeneous source. The TBS algorithm diverges when the sound-speed mismatch is ⪆20%, however, the CBS technique provides faithful result even beyond this limit. These protocols are iterative in nature and computationally expensive. Currently, MATLAB-based implementations are available to study PA emission from a single source mimicking a cell. However, efficient numerical implementation strategy is further needed particularly to calculate PA field from a tissue. Therefore, to develop insights, uniprocessor-based C codes were realized for these schemes. The PA field (in 2D) was computed at a distance 35 μm from a source (a light absorbing disc of radius 7.5 μm) over a frequency range from 7.32 to 512 MHz with a resolution of 7.32 MHz. The sound-speed within the source region was varied from vs = 1200, 1500 and 1800 m/s, but the same quantity for the ambient medium was fixed to v_f = 1500 m/s. The C program was found to be at least ten times slower than the corresponding MATLAB program. It may be because MATLAB inherently implements parallel computing while evaluating the forward and backward Fast Fourier Transforms (FFTs) associated with the Born series approaches. Multiprocessor-based FFTs and parallel nested loops are being incorporated into the C program for enhancement of its execution speed.

Proceedings Article | 11 August 2023 Paper

Estimation of photoacoustic spectra for normal and pathological red blood cells using a modified Green’s function approach

Ratan Saha, Ujjal Mandal

Proceedings Volume 12631, 1263109 (2023) https://doi.org/10.1117/12.2670933

KEYWORDS: Red blood cells, Photoacoustic spectroscopy, Inhomogeneities, Wave equations, Monte Carlo methods, Optoacoustics, Deformation

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The frequency domain Optoacoustic (OA) wave equation is inherently inhomogeneous. The first inhomogeneous term arises because of the OA effect (i.e., conversion of optical energy into acoustical energy). The second term appears due to sound-speed mismatch between the source and the ambient medium. The conventional Green’s function method works well in absence of the second term (i.e., acoustically homogeneous source). Recently, it has been shown that a Modified Green’s Function (MGF) approach provides faithful solution to the OA wave equation for an acoustically inhomogeneous source. Herein, we employ the MGF technique for accurate estimation of the OA spectra for normal and pathological red blood cells (RBCs). The shapes in 2D mimicking normal RBC, stomatocyte and echinocyte (with six equidistant identical spicules) were simulated (with constant area ≈ 16.5 μm² ) and subsequently, the OA spectra were computed over 10- 1000 MHz by evaluating the integral equation employing the Monte Carlo integration method. The OA spectrum for an equivalent disc was also calculated for comparison. The sound-speed within the source region was taken as 1639 m/s and that of the surrounding medium was chosen as 1500 m/s. The first minimum of the OA spectra for disc and echinocyte appeared almost at the same location (440 MHz) when probed from an angle, θ=π/4 with respect to the axis of symmetry. The locations for the first minimum became 280 and 390 MHz, respectively for normal RBC and stomatocyte (for θ=π/4). These 0A spectral features may be useful for morphological characterization of normal and deformed RBCs.

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