Quantitative evaluation of the impact of variation of optical parameters on the estimation of blood hematocrit and oxygen saturation for dual-wavelength photoacoustics.

Photoacoustic (PA) spectroscopy is considered to be one of the most effective ways to measure the levels of hematocrit (H) and oxygenation saturation (S O 2) of blood, which are essential for diagnosing blood-related illnesses. This simulation study aims to investigate the impact of individual optical parameters, i.e., optical absorption coefficient (µ a), scattering coefficient (µ s), and anisotropy factor (g), on the accuracy of this technique in estimating the blood properties. We first performed the Monte Carlo simulations, using realistic optical parameters, to obtain the fluence maps for various samples. The wavelengths of the incident light were chosen to be 532, 700, 1000, and 1064 nm. Thereafter, the k-Wave simulations were executed, incorporating those fluence maps to generate the PA signals. The blood properties were obtained using the PA signals. We introduced variations in µ a, µ s, and g ranging from -10% to +10%, -10% to +10%, and -5% to +1%, respectively, at 700 and 1000 nm wavelengths. One parameter, at both wavelengths, was changed at a time, keeping others fixed. Subsequently, we examined how accurately the blood parameters could be determined at physiological hematocrit levels. A 10% variation in µ a induces a 10% change in H estimation but no change in S O 2 determination. Almost no change has been seen for µ s variation. However, a 5% (-5% to 0%) variation in the g factor resulted in approximately 160% and 115% changes in the PA signal amplitudes at 700 and 1000 nm, respectively, leading to ≈125% error in hematocrit estimation and ≈14% deviation in S O 2 assessment when nominal S O 2=70%. It is clear from this study that the scattering anisotropy factor is a very sensitive parameter and a small change in its value can result in large errors in the PA estimation of blood properties. In the future, in vitro experiments with pathological blood (inducing variation in the g parameter) will be performed, and accordingly, the accuracy of the PA technique in quantifying blood H and S O 2 will be evaluated.

Photoacoustic Signal Simulation Using Discrete Particle Approach and its Application in Tomography.

A theoretical framework for photoacoustic (PA) signal simulation using a discrete particle approach is discussed, and the tomographic image reconstruction using such signals is reported. Various numerical phantoms in two dimensions were constructed by inserting monodisperse/polydisperse solid circles/disks of uniform strength occupying regular or random locations within the imaging region. In particular, a blood vessel network phantom was simulated by positioning solid circles mimicking red blood cells randomly within the vessel using a Monte Carlo method. The PA signal from a single disk was obtained by numerically evaluating the analytical formula, and then, such signals from many disks were summed up linearly to generate the resultant signals at detector locations. Classical backprojection and time-reversal algorithms were employed to form reconstructed images. Two model-based approaches, namely impulse response-based (IRB) and interpolation-based (IPB) methods, were also deployed for image reconstruction. Some standard parameters were calculated to assess the performance of these reconstruction algorithms. The simulation results demonstrate that the Monte Carlo method can be applied in practice for the fast simulation of tissue realization keeping microscopic details intact, and accordingly, PA signals can be calculated for photoacoustic tomography (PAT) imaging. Furthermore, the IRB technique produces images with superior quality and outperforms other algorithms.

A simulation study on the quantitative assessment of tissue microstructure with photoacoustics.

A detailed derivation of a quantity, defined as the acoustic power per unit solid angle far from the illuminated volume divided by the intensity of the incident light beam and termed as differential photoacoustic (PA) cross section, is presented. The expression for the differential PA cross section per unit absorbing volume retains two terms, namely, the coherent and the incoherent parts. The second part based on a correlation model can be employed to analyze the PA signal power spectrum for tissue characterization. The performances of the fluid sphere, Gaussian, and exponential correlation models in assessing the mean size and the variance in the optical absorption coefficients of absorbers were investigated by performing in silico experiments. It was possible to evaluate diameters of solid spherical absorbers with radii ≥ 20 µm with an accuracy of 10% for an analysis bandwidth of 5 to 50 MHz using the first two correlation models. The accuracy of estimation was about 22% for fluid spheres mimicking erythrocytes for the third correlation model for an analysis bandwidth of 5 to 100 MHz. The extracted values of average variance in the optical absorption coefficients demonstrated good correlation with the nominal values. This study suggests that the method presented here may be developed as a potential tissue characterization tool.

Effects of erythrocyte oxygenation on optoacoustic signals.

A theoretical model examining the effects of erythrocyte oxygenation on optoacoustic (OA) signals is presented. Each erythrocyte is considered as a fluid sphere and its optical absorption is defined by its oxygen saturation state. The OA field generated by a cell is computed by solving the wave equation in the frequency domain with appropriate boundary conditions. The resultant field from many cells is simulated by summing the pressure waves emitted by individual cells. A Monte Carlo algorithm generates 2-D spatially random distributions of oxygenated and deoxygenated erythrocytes. Oxygen saturation levels of oxygenated cells a assumed to be 100% and 0% for deoxygenated cells. The OA signal amplitude decreases monotonically for the 700-nm laser source and increases monotonically for 1000 nm optical radiation when blood oxygen saturation varies from 0 to 100%. An approximately sixfold decrease and fivefold increase of the OA signal amplitude were computed at those wavelengths, respectively. The OA spectral power in the low-frequency range (<10 MHz) and in the very high-frequency range (>100 MHz) decreases for 700 nm and increases for 1000 nm with increasing blood oxygen saturation. This model provides a theoretical framework to study the erythrocyte oxygenation-dependent OA signals.

Effects of cell spatial organization and size distribution on ultrasound backscattering.

In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 µm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 µm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.

A simulation study on photoacoustic signals from red blood cells.

A two dimensional simulation study was performed to investigate the photoacoustic signal properties of non-aggregated and aggregated erythrocytes. Spatial distributions of non-aggregated blood samples were generated by employing a Monte Carlo method and aggregated blood samples were simulated using a hexagonal packing scheme. For the non-aggregating case photoacoustic signals demonstrated a monotonic rise with hematocrit. For the aggregating case it was found that spectral (<20 MHz) intensity increased (11 dB at 15.6 MHz) when the aggregate size increased. This study strongly suggests that the assessment of erythrocyte aggregation level in human blood might be possible by using a photoacoustic spectroscopic method.

Assessment of accuracy of the structure-factor-size-estimator method in determining red blood cell aggregate size from ultrasound spectral backscatter coefficient.

A computer simulation study to produce ultrasonic backscatter coefficients (BSCs) from red blood cell (RBC) clusters is discussed. The simulation algorithm is suitable for generating non-overlapping, isotropic, and fairly identical RBC clusters. RBCs were stacked following the hexagonal close packing (HCP) structure to form a compact spherical aggregate. Such an aggregate was repeated and placed randomly under non-overlapping condition in the three-dimensional space to mimic an aggregated blood sample. BSCs were computed between 750 KHz and 200 MHz for samples of various cluster sizes at different hematocrits. Magnitudes of BSCs increased with mean aggregate sizes at low frequencies (<20 MHz). The accuracy of the structure-factor-size-estimator (SFSE) method in determining mean aggregate size and packing factor was also examined. A good correlation (R(2) ≥ 0.94) between the mean size of aggregates predicted by the SFSE and true size was found for each hematocrit. This study shows that for spherical aggregates there exists a region for each hematocrit where SFSE works most accurately. Typically, error of SFSE in estimating mean cluster size was <20% for dimensions between 14 and 17 µm at 40% hematocrit. This study suggests that the theoretical framework of SFSE is valid under the assumption of isotropic aggregates.

An increase in cellular size variance contributes to the increase in ultrasound backscatter during cell death.

This study aims to explain the contribution of changes in cellular size variance (CSV) to increases in ultrasound-integrated backscatter (UIB) measured from cell samples undergoing cell death. A Monte Carlo algorithm was used to compare simulations of 2D distributions of cells, uniform (CSV = 0) versus heterogeneous (CSV > 0) and the same mean cellular size (M ). UIB increased in arrangements with heterogeneous cellular sizes from 3.6dB (M = 20 mum, CSV = 0 microm/CSV = 18 microm) to 5.6 dB (M =10 microm, CSV = 0 microm/CSV = 8 microm). Experimentally, UIB (10 to 30 MHz) was measured from cell samples of four tumor cell lines viable and undergoing cell death after radiotherapy and chemotherapy treatment. An increase of 3.8-7.5 dB (p < 0.001) in UIB was measured from three cell lines. No increase in UIB was measured from one cell line. An increase in CSV was found for all cell samples after cell death. The results suggest that an increase in CSV could have a significant contribution to the increases measured in UIB after cell death in cell samples exposed to anticancer therapies.

Monte Carlo study on ultrasound backscattering by three-dimensional distributions of red blood cells.

A Monte Carlo study on ultrasound backscattering by red blood cells (RBCs) is presented for three-dimensional (3D) distributions of particles. The cells were treated as classical spherical particles and accordingly, the Boltzmann distribution was considered to describe probability distribution of energy states of a system composed of such particles. The well-known Metropolis algorithm can generate configurations according to that probability distribution and therefore, was employed in this study to simulate some realizations of both nonaggregating and aggregating RBCs. The study of nonaggregating particles was motivated to compare simulations with existing experimental results and consequently, to validate the model. In the case of aggregating RBCs, the interaction potential between cells was modeled with the Morse potential and the frequency-dependent backscattering coefficient (BSC) was investigated at different hematocrits (H, particle volume fractions). The impact of aggregation potential on the spectral slope (SS) was also evaluated. It is shown that BSC increased as the magnitude of aggregating potential was raised and the effect was more pronounced at higher hematocrits. Moreover, spectral slopes at nonaggregating and low aggregating conditions were found to be around 4, which is consistent with the Rayleigh scattering theory. However, it had diminished significantly, particularly at higher hematocrits as the magnitude of the attractive potential energy was raised. For instance, at H=40% SS dropped from 4.04 for nonaggregating particles to 3.62 at the highest aggregating potential considered in this study. Our results suggest that this 3D model is capable of reflecting the effects of RBC aggregation on BSC and SS.