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Following a comprehensive analysis of the historical literature, we model the geometry of the Stern$\unicode{x2013}$Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field and Monte Carlo methods, the atomic translational dynamics are simulated to produce the well-known quantized end-pattern with matching dimensions. The finite-element method used provides the most accurate description of the Stern$\unicode{x2013}$Gerlach magnetic field and end-pattern in the literature, matching the historically reported values and figures.

The transition from classical physics to quantum mechanics has been mysterious. Here, we derive the space-independent von Neumann equation for electron spin mathematically from the classical Bloch or Majorana--Bloch equation, which is also derived. Subsequently, the space-independent Schr\"odinger--Pauli equation is derived in both the quantum mechanical and recently developed co-quantum dynamic frameworks.

Optical imaging of blood flow yields critical functional insights into the circulatory system, but its clinical implementation has typically been limited to shallow depths (~1 millimeter) due to light scattering in biological tissue. Here, we present photoacoustic noninvasive Doppler angiography (PANDA) for deep blood flow imaging. PANDA synergizes the photoacoustic and Doppler effects to generate color Doppler velocity and power Doppler blood flow maps of the vascular lumen. Our results demonstrate PANDA's ability to measure blood flow in vivo up to one centimeter in depth, marking approximately an order of magnitude improvement over existing high-resolution pure optical modalities. PANDA enhances photoacoustic flow imaging by increasing depth and enabling cross-sectional blood vessel imaging. We also showcase PANDA's clinical feasibility through three-dimensional imaging of blood flow in healthy subjects and a patient with varicose veins. By integrating the imaging system onto a mobile platform, we have designed PANDA to be a portable modality that is primed for expedient clinical translation. PANDA offers noninvasive, single modality imaging of hemoglobin and blood flow with three-dimensional capability, facilitating comprehensive assessment of deep vascular dynamics in humans., Comment: 38 pages, 7 main figures, 10 supplementary figures

Noninvasive transcranial photoacoustic computed tomography (PACT) of the human brain, despite its clinical potential, remains impeded by the acoustic distortion induced by the human skull. The distortion, which is attributed to the markedly different material properties of the skull relative to soft tissue, results in heavily aberrated PACT images -- a problem that has remained unsolved in the past two decades. Herein, we report the first successful experimental demonstration of the de-aberration of PACT images through an ex-vivo adult human skull using a homogeneous elastic model for the skull. Using only the geometry, position, and orientation of the skull, we accurately de-aberrate the PACT images of light-absorbing phantoms acquired through an ex-vivo human skull, in terms of the recovered phantom features, for different levels of phantom complexity and positions. Our work addresses the longstanding challenge of skull-induced aberrations in transcranial PACT and advances the field towards unlocking the full potential of transcranial human brain PACT., Comment: 11 pages, 3 figures

Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to limited sensor coverage or due to the density of the transducer array. Such cases call for solving an ill-posed inverse reconstruction problem. In this work, we use score-based diffusion models to solve the inverse problem of reconstructing an image from limited PAT measurements. The proposed approach allows us to incorporate an expressive prior learned by a diffusion model on simulated vessel structures while still being robust to varying transducer sparsity conditions., Comment: 5 pages

We developed a system for whole-body human ultrasound tomography in reflection and transmission modes. A custom 512-element ultrasound receiver array with a rotating single-element ultrasound transmitter are used to generate 2D isotropically resolved images across the entire human cross-section. We demonstrate this technique in regions such as the abdomen and legs in healthy volunteers. Compared to handheld-probe-based ultrasonography, this approach provides a substantially larger field of view, depends less on operator training, and obtains quantitative tissue parameter profiles in addition to reflectivity images. Whole-body ultrasound tomography could be valuable in applications such as organ disease screening, image-guided needle biopsy, and treatment monitoring., Comment: 8 pages, 4 figures

Photoacoustic computed tomography (PACT) is emerging as a new technique for functional brain imaging, primarily due to its capabilities in label-free hemodynamic imaging. Despite its potential, the transcranial application of PACT has encountered hurdles, such as acoustic attenuations and distortions by the skull and limited light penetration through the skull. To overcome these challenges, we have engineered a PACT system that features a densely packed hemispherical ultrasonic transducer array with 3072 channels, operating at a central frequency of 1 MHz. This system allows for single-shot 3D imaging at a rate equal to the laser repetition rate, such as 20 Hz. We have achieved a single-shot light penetration depth of approximately 9 cm in chicken breast tissue utilizing a 750 nm laser (withstanding 3295-fold light attenuation and still retaining an SNR of 74) and successfully performed transcranial imaging through an ex vivo human skull using a 1064 nm laser. Moreover, we have proven the capacity of our system to perform single-shot 3D PACT imaging in both tissue phantoms and human subjects. These results suggest that our PACT system is poised to unlock potential for real-time, in vivo transcranial functional imaging in humans.

In many clinical conditions, such as head trauma, stroke, and low cardiac output states, the brain is at risk for hypoxic-ischemic injury. The metabolic rate and oxygen consumption of the brain are reflected in internal jugular venous oxygen saturation (sijvO2). The current gold standard for monitoring brain oxygenation is invasive; it requires jugular vein catheterization under fluoroscopic guidance and therefore is rarely used. Photoacoustic (PA) measurement, on the other hand, can estimate the oxygen consumption of the brain non-invasively in real time. Such a convenient method can potentially aid earlier detection and prevention of impending hypoxic brain injury. A dual-wavelength photoacoustic tomography (PAT) and ultrasound imaging (US) system was used to image the internal jugular vein (IJV) and estimate the sijvO2 in seven healthy volunteers. The system captured simultaneous co-registered PAT and US images at a rate of five frames per second. For each volunteer, the internal jugular vein was identified under ultrasound guidance, then, additional PA images from two optical wavelengths were collected and used to estimate the oxygen saturation of the internal jugular vein. For each volunteer, the oxygen saturation was calculated from transverse and longitudinal views of the internal jugular vein. The average sijvO2 was 72 +/- 7 %. The preliminary results are encouraging and agree with those reported in the literature. Photoacoustic images were successfully used to calculate the blood hemoglobin oxygen saturation in the internal jugular vein. These results raise confidence that this emerging technology can be used clinically for accurate, noninvasive estimation of sijvO2. In addition, the fast co-registration with US images makes the technique suitable for studying the temporal variations of oxygen saturation in response to physiologic challenges in clinical settings.

Objective: Strain elastography and shear wave elastography are two commonly used methods to quantify cervical elasticity; however, they have limitations. Strain elastography is effective in showing tissue elasticity distribution in a single image, but the absence of stress information causes difficulty in comparing the results acquired from different imaging sessions. Shear wave elastography is effective in measuring shear wave speed (an intrinsic tissue property correlated with elasticity) in relatively homogeneous tissue, such as in the liver. However, for inhomogeneous tissue in the cervix, the shear wave speed measurement is less robust. To overcome these limitations, we develop a quantitative cervical elastography system by adding a stress sensor to an ultrasound imaging system. Methods: In an imaging session for quantitative cervical elastography, we use the transvaginal ultrasound imaging system to record B-mode images of the cervix showing its deformation and use the stress sensor to record the probe-surface stress simultaneously. We develop a correlation-based automatic feature tracking algorithm to quantify the deformation, from which the strain is quantified. After each imaging session, we calibrate the stress sensor and transform its measurement to true stress. Applying a linear regression to the stress and strain, we obtain an approximation of the cervical Young's modulus. Results: We validate the accuracy and robustness of this elastography system using phantom experiments. Applying this system to pregnant participants, we observe significant softening of the cervix during pregnancy (p-value < 0.001) with the cervical Young's modulus decreasing 3.95% per week. We estimate that geometric mean values of cervical Young's moduli during the first (11 to 13 weeks), second, and third trimesters are 13.07 kPa, 7.59 kPa, and 4.40 kPa, respectively., Comment: 26 pages, 8 figures, 1 table

Quantum imaging can potentially provide certain advantages over classical imaging. Thus far, however, the signal-to-noise ratios (SNRs) are poor; the resolvable pixel counts are low; biological organisms have not been imaged; birefringence has not been quantified. Here, we introduce quantum imaging by coincidence from entanglement (ICE). Utilizing spatially and polarization entangled photon pairs, ICE exhibits higher SNRs, greater resolvable pixel counts, imaging of biological organisms, and ghost birefringence quantification; it also enables 25 times greater suppression of stray light than classical imaging. ICE can potentially empower quantum imaging towards new applications in life sciences and remote sensing., Comment: 57 pages, 4 figures, 18 supplementary figures, 7 supplementary notes, 1 supplementary table

Entangled biphoton sources exhibit nonclassical characteristics and have been applied to imaging techniques such as ghost imaging, quantum holography, and quantum optical coherence tomography. The development of wide-field quantum imaging to date has been hindered by low spatial resolutions, speeds, and contrast-to-noise ratios (CNRs). Here, we present quantum microscopy by coincidence (QMC) with balanced pathlengths, which enables super-resolution imaging at the Heisenberg limit with substantially higher speeds and CNRs than existing wide-field quantum imaging methods. QMC benefits from a configuration with balanced pathlengths, where a pair of entangled photons traversing symmetric paths with balanced optical pathlengths in two arms behave like a single photon with half the wavelength, leading to 2-fold resolution improvement. Concurrently, QMC resists stray light up to 155 times stronger than classical signals. The low intensity and entanglement features of biphotons in QMC promise nondestructive bioimaging. QMC advances quantum imaging to the microscopic level with significant improvements in speed and CNR toward bioimaging of cancer cells. We experimentally and theoretically prove that the configuration with balanced pathlengths illuminates an avenue for quantum-enhanced coincidence imaging at the Heisenberg limit., Comment: 20 pages, 4 figures; Supplementary Information 15 pages, 9 figures

The multi-stage Stern$\unicode{x2013}$Gerlach experiment conducted by Frisch and Segr\`e includes two cascaded quantum measurements with a nonadiabatic flipper in between. The Frisch and Segr\`e experiment has been modeled analytically by Majorana without the nuclear effect and subsequently revised by Rabi with the hyperfine interaction. However, the theoretical predictions do not match the experimental observation accurately. Here, we numerically solve the standard quantum mechanical model, via the von Neumann equation, including the hyperfine interaction for the time evolution of the spin. Thus far, the coefficients of determination from the standard quantum mechanical model without using free parameters are still low, indicating a mismatch between the theory and the experiment. Non-standard variants that improve the match are explored for discussion., Comment: 11 pages, 6 figures

Non-invasive imaging of deep blood vessels for mapping hemodynamics remains an open quest in biomedical optical imaging. Although pure optical imaging techniques offer rich optical contrast of blood and have been reported to measure blood flow, they are generally limited to surface imaging within the optical diffusion limit of about one millimeter. Herein, we present photoacoustic vector tomography (PAVT), breaking through the optical diffusion limit to image deep blood flow with speed and direction quantification. PAVT synergizes the spatial heterogeneity of blood and the photoacoustic contrast; it compiles successive single-shot, wide-field photoacoustic images to directly visualize the frame-to-frame propagation of the blood with pixel-wise flow velocity estimation. We demonstrated in vivo that PAVT allows hemodynamic quantification of deep blood vessels at five times the optical diffusion limit (more than five millimeters), leading to vector mapping of blood flow in humans. By offering the capability for deep hemodynamic imaging with optical contrast, PAVT may become a powerful tool for monitoring and diagnosing vascular diseases and mapping circulatory system function.

We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern$\unicode{x2013}$Gerlach (SG) experiment conducted by R. Frisch and E. Segr\`e. This experiment consists of two Stern$\unicode{x2013}$Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch$\unicode{x2013}$Segr\`e experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schr\"odinger equation. Our simulation outcome agrees with the Frisch$\unicode{x2013}$Segr\`e experimental observation and supports CQD as a potential model for electron spin evolution and collapse., Comment: 13 pages, 3 figures

We numerically study the spin flip in the Frisch$\unicode{x2013}$Segr\`e experiment, the first multi-stage Stern$\unicode{x2013}$Gerlach experiment, within the context of the novel co-quantum dynamics theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segr\`e in 1933, which has so far lacked theoretical predictions., Comment: 9 pages, 6 figures

In the classic multi-stage Stern$-$Gerlach experiment conducted by Frisch and Segr\`e, the Majorana (Landau$-$Zener) and Rabi formulae diverge afar from the experimental observation while the physical mechanism for electron-spin collapse remains unidentified. Here, introducing the physical co-quantum concept provides a plausible physical mechanism and predicts the experimental observation in absolute units without fitting (i.e., no parameters adjusted) with a p-value less than one per million, which is the probability that the co-quantum theory happens to match the experimental observation purely by chance. Further, the co-quantum concept is corroborated by statistically reproducing exactly the wave function, density operator, and uncertainty relation for electron spin in Stern$-$Gerlach experiments.

Herein we report the first in-human transcranial imaging of brain function using photoacoustic computed tomography. Functional responses to benchmark motor tasks were imaged on both the skull-less and the skull-intact hemispheres of a hemicraniectomy patient. The observed brain responses in these preliminary results demonstrate the potential of photoacoustic computed tomography for achieving transcranial functional imaging.

Speckles arise when coherent light interacts with biological tissues. Information retrieval from speckles is desired yet challenging, requiring understanding or mapping of the multiple scattering process, or reliable capability to reverse or compensate for the scattering-induced phase distortions. In whatever situation, insufficient sampling of speckles undermines the encoded information, impeding successful object reconstruction from speckle patterns. In this work, we propose a deep learning method to combat the physical limit: the sub-Nyquist sampled speckles (~14 below the Nyquist criterion) are interpolated up to a well-resolved level (1024 times more pixels to resolve the same FOV) with smoothed morphology fine-textured. More importantly, the lost information can be retraced, which is impossible with classic interpolation or any existing methods. The learning network inspires a new perspective on the nature of speckles and a promising platform for efficient processing or deciphering of massive scattered optical signals, enabling widefield high-resolution imaging in complex scenarios.

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units (GPUs) are also developed. The developed numerical framework is validated and investigated in computer-simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications.

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. If the object possesses spatially variant acoustic properties that are unaccounted for by the reconstruction method, the estimated image can contain distortions. While reconstruction methods have recently been developed to compensate for this effect, they generally require the object's acoustic properties to be known a priori. To circumvent the need for detailed information regarding an object's acoustic properties, we previously proposed a half-time reconstruction method for PACT. A half-time reconstruction method estimates the PACT image from a data set that has been temporally truncated to exclude the data components that have been strongly aberrated. However, this method can be improved upon when the approximate sizes and locations of isolated heterogeneous structures, such as bones or gas pockets, are known. To address this, we investigate PACT reconstruction methods that are based on a variable data truncation (VDT) approach. The VDT approach represents a generalization of the half-time approach, in which the degree of temporal truncation for each measurement is determined by the distance between the corresponding ultrasonic transducer location and the nearest known bone or gas void location. Computer-simulated and experimental data are employed to demonstrate the effectiveness of the approach in mitigating artifacts due to acoustic heterogeneities.