Pillar data-acquisition strategies for cryo-electron tomography of beam-sensitive biological samples.

For cryo-electron tomography (cryo-ET) of beam-sensitive biological specimens, a planar sample geometry is typically used. As the sample is tilted, the effective thickness of the sample along the direction of the electron beam increases and the signal-to-noise ratio concomitantly decreases, limiting the transfer of information at high tilt angles. In addition, the tilt range where data can be collected is limited by a combination of various sample-environment constraints, including the limited space in the objective lens pole piece and the possible use of fixed conductive braids to cool the specimen. Consequently, most tilt series are limited to a maximum of ±70°, leading to the presence of a missing wedge in Fourier space. The acquisition of cryo-ET data without a missing wedge, for example using a cylindrical sample geometry, is hence attractive for volumetric analysis of low-symmetry structures such as organelles or vesicles, lysis events, pore formation or filaments for which the missing information cannot be compensated by averaging techniques. Irrespective of the geometry, electron-beam damage to the specimen is an issue and the first images acquired will transfer more high-resolution information than those acquired last. There is also an inherent trade-off between higher sampling in Fourier space and avoiding beam damage to the sample. Finally, the necessity of using a sufficient electron fluence to align the tilt images means that this fluence needs to be fractionated across a small number of images; therefore, the order of data acquisition is also a factor to consider. Here, an n-helix tilt scheme is described and simulated which uses overlapping and interleaved tilt series to maximize the use of a pillar geometry, allowing the entire pillar volume to be reconstructed as a single unit. Three related tilt schemes are also evaluated that extend the continuous and classic dose-symmetric tilt schemes for cryo-ET to pillar samples to enable the collection of isotropic information across all spatial frequencies. A fourfold dose-symmetric scheme is proposed which provides a practical compromise between uniform information transfer and complexity of data acquisition.

Parakeet: a digital twin software pipeline to assess the impact of experimental parameters on tomographic reconstructions for cryo-electron tomography.

In cryo-electron tomography (cryo-ET) of biological samples, the quality of tomographic reconstructions can vary depending on the transmission electron microscope (TEM) instrument and data acquisition parameters. In this paper, we present Parakeet, a 'digital twin' software pipeline for the assessment of the impact of various TEM experiment parameters on the quality of three-dimensional tomographic reconstructions. The Parakeet digital twin is a digital model that can be used to optimize the performance and utilization of a physical instrument to enable in silico optimization of sample geometries, data acquisition schemes and instrument parameters. The digital twin performs virtual sample generation, TEM image simulation, and tilt series reconstruction and analysis within a convenient software framework. As well as being able to produce physically realistic simulated cryo-ET datasets to aid the development of tomographic reconstruction and subtomogram averaging programs, Parakeet aims to enable convenient assessment of the effects of different microscope parameters and data acquisition parameters on reconstruction quality. To illustrate the use of the software, we present the example of a quantitative analysis of missing wedge artefacts on simulated planar and cylindrical biological samples and discuss how data collection parameters can be modified for cylindrical samples where a full 180° tilt range might be measured.

Fast Bilateral Filtering for Denoising Large 3D Images.

A fast implementation of bilateral filtering is presented, which is based on an optimal expansion of the filter kernel into a sum of factorized terms. These terms are computed by minimizing the expansion error in the mean-square-error sense. This leads to a simple and elegant solution in terms of eigenvectors of a square matrix. In this way, the bilateral filter is applied through computing a few Gaussian convolutions, for which very efficient algorithms are readily available. Moreover, the expansion functions are optimized for the histogram of the input image, leading to improved accuracy. It is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions. Experimental validation is carried out in the context of digital rock imaging. Results on large 3D images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering.

Polycontinuous geometries for inverse lipid phases with more than two aqueous network domains.

Inverse bicontinuous cubic phases with two aqueous network domains separated by a smooth bilayer are firmly established as equilibrium phases in lipid/water systems. The purpose of this article is to highlight the generalisations of these bicontinuous geometries to polycontinuous geometries, which could be realised as lipid mesophases with three or more network-like aqueous domains separated by a branched bilayer. An analysis of structural homogeneity in terms of bilayer width variations reveals that ordered polycontinuous geometries are likely candidates for lipid mesophase structures, with similar chain packing characteristics to the inverse micellar phases (that once were believed not to exist due to high packing frustration). The average molecular shape required by global geometry to form these multi-network phases is quantified by the surfactant shape parameter, v/(al); we find that it adopts values close to those of the known lipid phases. We specifically analyse the 3etc(187 193) structure of hexagonal symmetry P6(3) /mcm with three aqueous domains, the 3dia(24 220) structure of cubic symmetry I43d composed of three distorted diamond networks, the cubic chiral 4srs(24 208) with cubic symmetry P4232 and the achiral 4srs(5 133) structure of symmetry P42/nbc, each consisting of four intergrown undistorted copies of the srs net (the same net as in the QII(G) gyroid phase). Structural homogeneity is analysed by a medial surface approach assuming that the headgroup interfaces are constant mean curvature surfaces. To facilitate future experimental identification, we provide simulated SAXS scattering patterns that, for the 4srs(24 208) and 3dia(24 220) structures, bear remarkable similarity to those of bicontinuous QII(G)-gyroid and QII(D)-diamond phases, with comparable lattice parameters and only a single peak that cannot be indexed to the well-established structures. While polycontinuous lipid phases have, to date, not been reported, the likelihood of their formation is further indicated by the reported observation of a solid tricontinuous mesoporous silicate structure, termed IBN-9, which formed in the presence of surfactants [Han et al., Nat. Chem., 2009, 1, 123].

Extending reference scan drift correction to high-magnification high-cone-angle tomography.

The reference scan method is a simple yet powerful method for measuring spatial drift of the x-ray spot during a low-cone-angle µ-CT experiment. As long as the drift is smooth, and occurring on a time scale that is long compared to the acquisition time of each projection, this method provides a way to compensate for the drift by applying 2D in-plane translations to the radiographs. Here we show that this compensation may be extended to the regime of high-magnification, high-cone-angle CT experiments where source drift perpendicular to the detector plane can cause significant magnification changes throughout the acquisition.

Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach.

The reconstruction of images in photoacoustic tomography is reliant on specifying the speed of sound within the propagation medium. However, for in vivo imaging, this value is not normally accurately known. Here, an autofocus approach for automatically selecting the sound speed is proposed. This is based on maximizing the sharpness of the reconstructed image as quantified by a focus function. Several focus functions are investigated, and their performance is discussed. The method is demonstrated using phantom measurements made in a medium with a known sound speed and in vivo measurements of the vasculature in the flank of an adult mouse.

A bicontinuous mesophase geometry with hexagonal symmetry.

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists.

Dynamic tomography with a priori information.

We present "dynamic tomography" algorithms that allow for the high-resolution, time-resolved imaging of dynamic (i.e., continuously time evolving) complex systems at existing x-ray micro-CT facilities. The behavior of complex systems is constrained by the underlying physics. By exploiting a priori knowledge of the geometry of the physical process being studied to allow the use of sophisticated iterative reconstruction techniques that incorporate constraints, we improve on current frame rates by at least an order of magnitude. This allows time-resolved imaging of previously intractable processes, such as two-phase fluid flow. We present reconstructions from experimental data collected at the Australian National University x-ray micro-CT facility.

A novel lyotropic liquid crystal formed by triphilic star-polyphiles: hydrophilic/oleophilic/fluorophilic rods arranged in a 12.6.4. tiling.

Triphilic star-polyphiles are short-chain oligomeric molecules with a radial arrangement of hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number of liquid crystalline structures when mixed with water. In this contribution we focus on a hexagonal liquid crystalline mesophase found in star-polyphiles as compared to the corresponding double-chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact demixed in these star-polyphile systems, or whether both hydrocarbon and fluorocarbon chains are miscible, leading to a single hydrophobic domain, making the star-polyphile effectively amphiphilic. We report SANS contrast variation data that are compatible only with the presence of three distinct immiscible domains within this hexagonal mesophase, confirming that these star-polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3-phase systems. Quantitative comparison with scattering simulations shows that the experimental data are in very good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains) are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic domains and fluorophilic quadrangular prismatic domains.

Refraction corrected transmission ultrasound computed tomography for application in breast imaging.

PURPOSE: We present an iterative framework for CT reconstruction from transmission ultrasound data which accurately and efficiently models the strong refraction effects that occur in our target application: Imaging the female breast. METHODS: Our refractive ray tracing framework has its foundation in the fast marching method (FNMM) and it allows an accurate as well as efficient modeling of curved rays. We also describe a novel regularization scheme that yields further significant reconstruction quality improvements. A final contribution is the development of a realistic anthropomorphic digital breast phantom based on the NIH Visible Female data set. RESULTS: Our system is able to resolve very fine details even in the presence of significant noise, and it reconstructs both sound speed and attenuation data. Excellent correspondence with a traditional, but significantly more computationally expensive wave equation solver is achieved. CONCLUSIONS: Apart from the accurate modeling of curved rays, decisive factors have also been our regularization scheme and the high-quality interpolation filter we have used. An added benefit of our framework is that it accelerates well on GPUs where we have shown that clinical 3D reconstruction speeds on the order of minutes are possible.

An eigenfunction method for reconstruction of large-scale and high-contrast objects.

A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.

Aberration in nonlinear acoustic wave propagation.

Theory and simulations are presented indicating that imaging at the second-harmonic frequency does not solve the problem of ultrasonic wave aberration. The nonlinearity of acoustic wave propagation in biological tissue is routinely exploited in medical imaging because the improved contrast resolution leads to better image quality in many applications. The major sources of acoustic noise in ultrasound images are aberration and multiple reflections between the transducer and tissue structures (reverberations), both of which are the result of spatial variations in the acoustic properties of the tissue. These variations mainly occur close to the body surface, i.e., the body wall. As a result, the nonlinearly generated, second harmonic is believed to alleviate both reverberation and aberration because it is assumed that the second harmonic is mainly generated after the body wall. However, in the case of aberration, the second harmonic is generated by an aberrated source. Thus the second harmonic experiences considerable aberration at all depths, originating from this source. The results in this paper show that the second harmonic experiences similar aberration as its generating source, the first harmonic.

Computer simulation of forward wave propagation in soft tissue.

A method for simulating forward wavefront propagation in heterogeneous tissue is discussed. The intended application of this method is for the study of aberration produced when performing ultrasound imaging through a layer of soft tissue. A one-way wave equation that permits smooth variation in all acoustically important variables is derived. This equation also describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent relaxation. A numerical solution to this equation is found by means of operator splitting and propagation along the spatial depth coordinate. The numerical solution is accurate when compared to analytical solutions for special cases, and when compared to numerical solutions of the full wave equation by other methods. The presented implementation provides a fast numerical method for studying the impact of aberration in medical ultrasound imaging through soft tissue--both on the transmitted beam and the nonlinearly generated harmonic beam.

Iteration of transmit-beam aberration correction in medical ultrasound imaging.

Simulations of iterative transmit-beam aberration correction using a time-delay and amplitude filter have been performed to study the convergence of such a process. Aberration in medical ultrasonic imaging is usually modeled by arrival-time and amplitude fluctuations concentrated on the transducer array. This is an approximation of the physical aberration process, and may be applied to correct the transmitted signal using a time-delay and amplitude filter. Estimation of such a filter has proven difficult in the presence of severe aberration. Presented here is an iterative approach, whereby a filter estimate is applied to correct the transmit-beam. This beam induces acoustic backscatter better suited for arrival-time and amplitude estimation, thus facilitating an improved filter estimate. Two correlation-based methods for estimating arrival-time and amplitude fluctuations in received echoes from random scatterers were employed. Aberration was introduced using eight models emulating aberration produced by the human abdominal wall. Results show that only a few iterations are needed to obtain corrected transmit-beam profiles comparable to those of an ideal aberration correction filter. Furthermore, a previously developed focusing criterion is found to quantify the convergence accurately.

Spectral estimation for characterization of acoustic aberration.

Spectral estimation based on acoustic backscatter from a motionless stochastic medium is described for characterization of aberration in ultrasonic imaging. The underlying assumptions for the estimation are: The correlation length of the medium is short compared to the length of the transmitted acoustic pulse, an isoplanatic region of sufficient size exists around the focal point, and the backscatter can be modeled as an ergodic stochastic process. The motivation for this work is ultrasonic imaging with aberration correction. Measurements were performed using a two-dimensional array system with 80 x 80 transducer elements and an element pitch of 0.6 mm. The f number for the measurements was 1.2 and the center frequency was 3.0 MHz with a 53% bandwidth. Relative phase of aberration was extracted from estimated cross spectra using a robust least-mean-square-error method based on an orthogonal expansion of the phase differences of neighboring wave forms as a function of frequency. Estimates of cross-spectrum phase from measurements of random scattering through a tissue-mimicking aberrator have confidence bands approximately +/- 5 degrees wide. Both phase and magnitude are in good agreement with a reference characterization obtained from a point scatterer.

Estimation of ultrasound wave aberration with signals from random scatterers.

A method for estimating waveform aberration from random scatterers in medical ultrasound imaging has been derived and its properties investigated using two-dimensional simulations. The method uses a weighted and modified cross-spectrum in order to estimate arrival time and amplitude fluctuations from received signals. The arrival time and amplitude fluctuations were used in a time delay, and a time delay and amplitude aberration correction filter, for evaluation of the retransmitted aberration corrected signal. Different types of aberration have been used in this study. First, aberration was concentrated on the plane of the transmitting/receiving array. Second, aberration was generated with a distributed aberrator. Both conditions emulated aberration from the human abdominal wall. Results show that for the concentrated aberrator, arrival time and amplitude fluctuations were estimated in close agreement with reference values. The reference values were obtained from simulations with a point source in the focal point of the array. Correction of the transmitted signal with a time delay, and a time delay and amplitude filter produced approximately equal correction as with point source estimates. For the distributed aberrator, the estimator performance degraded significantly. Arrival time and amplitude fluctuations deviated from reference values, leading to a limited correction of the retransmitted signal.

Eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging.

Presented here is a characterization of aberration in medical ultrasound imaging. The characterization is optimal in the sense of maximizing the expected energy in a modified beamformer output of the received acoustic backscatter. Aberration correction based on this characterization takes the form of an aberration correction filter. The situation considered is frequently found in applications when imaging organs through a body wall: aberration is introduced in a layer close to the transducer, and acoustic backscatter from a scattering region behind the body wall is measured at the transducer surface. The scattering region consists of scatterers randomly distributed with very short correlation length compared to the acoustic wavelength of the transmit pulse. The scatterer distribution is therefore assumed to be delta correlated. This paper shows how maximizing the expected energy in a modified beamformer output signal naturally leads to eigenfunctions of a Fredholm integral operator, where the associated kernel function is a spatial correlation function of the received stochastic signal. Aberration characterization and aberration correction are presented for simulated data constructed to mimic aberration introduced by the abdominal wall. The results compare well with what is obtainable using data from a simulated point source.