Model-based image reconstruction techniques yield better quantitative accuracy in photoacoustic image reconstruction. In this work, an exponential filtering of singular values was proposed for carrying out the image reconstruction in photoacoustic tomography. The results were compared with widely popular Tikhonov regularization, time reversal, and the state of the art least-squares QR-based reconstruction algorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown that exponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover, the proposed filtering approach was observed to be less biased toward the regularization parameter and did not come with any additional computational burden as it was implemented within the Tikhonov filtering framework. It was also shown that the standard Tikhonov filtering becomes an approximation to the proposed exponential filtering.
The model-based image reconstruction techniques for photoacoustic (PA) tomography require an explicit regularization. An error estimate (?2) minimization-based approach was proposed and developed for the determination of a regularization parameter for PA imaging. The regularization was used within Lanczos bidiagonalization framework, which provides the advantage of dimensionality reduction for a large system of equations. It was shown that the proposed method is computationally faster than the state-of-the-art techniques and provides similar performance in terms of quantitative accuracy in reconstructed images. It was also shown that the error estimate (?2) can also be utilized in determining a suitable regularization parameter for other popular techniques such as Tikhonov, exponential, and nonsmooth (?1 and total variation norm based) regularization methods.
Deep vein thrombosis is a common vascular disease that can lead to pulmonary embolism and death. The early diagnosis and clot age staging are important parameters for reliable therapy planning. This article presents an acoustic radiation force induced resonance elastography method for the viscoelastic characterization of clotting blood. The physical concept of this method relies on the mechanical resonance of the blood clot occurring at specific frequencies. Resonances are induced by focusing ultrasound beams inside the sample under investigation. Coupled to an analytical model of wave scattering, the ability of the proposed method to characterize the viscoelasticity of a mimicked venous thrombosis in the acute phase is demonstrated. Experiments with a gelatin-agar inclusion sample of known viscoelasticity are performed for validation and establishment of the proof of concept. In addition, an inversion method is applied in-vitro for the kinetic monitoring of the blood coagulation process of six human blood samples obtained from two volunteers. The computed elasticity and viscosity values of blood samples at the end of the 90 min kinetics were estimated at 411 ± 71 Pa and 0.25 ± 0.03 Pa.s for volunteer #1, and 387 ± 35 Pa and 0.23 ± 0.02 Pa.s for volunteer #2, respectively. The proposed method allowed reproducible time-varying thrombus viscoelastic measurements from samples having physiological dimensions.
The attenuation of near-infrared (NIR) light intensity as it propagates in a turbid medium like biological tissue is described by modified the Beer–Lambert law (MBLL). The MBLL is generally used to quantify the changes in tissue chromophore concentrations for NIR spectroscopic data analysis. Even though MBLL is effective in terms of providing qualitative comparison, it suffers from its applicability across tissue types and tissue dimensions. In this work, we introduce Lambert-W function-based modeling for light propagation in biological tissues, which is a generalized version of the Beer–Lambert model. The proposed modeling provides parametrization of tissue properties, which includes two attenuation coefficients μ0 and η. We validated our model against the Monte Carlo simulation, which is the gold standard for modeling NIR light propagation in biological tissue. We included numerous human and animal tissues to validate the proposed empirical model, including an inhomogeneous adult human head model. The proposed model, which has a closed form (analytical), is first of its kind in providing accurate modeling of NIR light propagation in biological tissues.
The limited data photoacoustic image reconstruction problem is typically solved using either weighted or ordinary least squares (LS), with regularization term being added for stability, which account only for data imperfections (noise). Numerical modeling of acoustic wave propagation requires discretization of imaging region and is typically developed based on many assumptions, such as speed of sound being constant in the tissue, making it imperfect. In this work, two variants of total least squares (TLS), namely ordinary TLS and Sparse TLS were developed, which account for model imperfections. The ordinary TLS is implemented in the Lanczos bidiagonalization framework to make it computationally efficient. The Sparse TLS utilizes the total variation penalty to promote recovery of high frequency components in the reconstructed image. The Lanczos truncated TLS (Lanczos T-TLS) and Sparse TLS methods were compared with the recently established state-of-the-art methods, such as Lanczos Tikhonov and Exponential Filtering. The TLS methods exhibited better performance for experimental data as well as in cases where modeling errors were present, such as few acoustic detectors malfunctioning and speed of sound variations. Also, the TLS methods does not require any prior information about the errors present in the model or data, making it attractive for real-time scenarios.
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