Slice Dimension Research Articles

Simulating multiple variability in spatially resolved transcriptomics with scCube

A pressing challenge in spatially resolved transcriptomics (SRT) is to benchmark the computational methods. A widely-used approach involves utilizing simulated data. However, biases exist in terms of the currently available simulated SRT data, which seriously affects the accuracy of method evaluation and validation. Herein, we present scCube (https://github.com/ZJUFanLab/scCube), a Python package for independent, reproducible, and technology-diverse simulation of SRT data. scCube not only enables the preservation of spatial expression patterns of genes in reference-based simulations, but also generates simulated data with different spatial variability (covering the spatial pattern type, the resolution, the spot arrangement, the targeted gene type, and the tissue slice dimension, etc.) in reference-free simulations. We comprehensively benchmark scCube with existing single-cell or SRT simulators, and demonstrate the utility of scCube in benchmarking spot deconvolution, gene imputation, and resolution enhancement methods in detail through three applications.

The Potential of Phase Constraints for Non-Fourier Radiofrequency-Encoded MRI.

In modern magnetic resonance imaging, it is common to use phase constraints to reduce sampling requirements along Fourier-encoded spatial dimensions. In this work, we investigate whether phase constraints might also be beneficial to reduce sampling requirements along spatial dimensions that are measured using non-Fourier encoding techniques, with direct relevance to approaches that use tailored spatially-selective radiofrequency (RF) pulses to perform spatial encoding along the slice dimension in a 3D imaging experiment. In the first part of the paper, we use the Cramér-Rao lower bound to examine the potential estimation theoretic benefits of using phase constraints. The results suggest that phase constraints can be used to improve experimental efficiency and enable acceleration, but only if the RF encoding matrix is complex-valued and appropriately designed. In the second part of the paper, we use simulations of RF-encoded data to test the benefits of phase constraints combined with optimized RF-encodings, and find that the theoretical benefits are indeed borne out empirically. These results provide new insights into the potential benefits of phase constraints for RF-encoded data, and provide a solid theoretical foundation for future practical explorations.

The effect of and correction for through-slice dephasing on 2D gradient-echo double angle mapping.

To show that variations through slice and slice profile effects are two major confounders affecting 2D dual angle maps using gradient-echo signals and thus need to be corrected to obtain accurate maps. The 2D gradient-echo transverse complex signal was Bloch-simulated and integrated across the slice dimension including nonlinear variations in inhomogeneities through slice. A nonlinear least squares fit was used to find the factor corresponding to the best match between the two gradient-echo signals experimental ratio and the Bloch-simulated ratio. The correction was validated in phantom and in vivo at 3T. For our RF excitation pulse, the error in the factor scales by approximately 3.8% for every 10 Hz/cm variation in along the slice direction. Higher accuracy phantom maps were obtained after applying the proposed correction; the root mean square error relative to the gold standard decreased from 6.4% to 2.6%. In vivo whole-liver maps using the corrected map registered a significant decrease in gradient through slice. inhomogeneities varying through slice were seen to have an impact on the accuracy of 2D double angle maps using gradient-echo sequences. Consideration of this confounder is crucial for research relying on accurate knowledge of the true excitation flip angles, as is the case of mapping using a spoiled gradient recalled echo sequence.

An improved deep dilated convolutional neural network for seismic facies interpretation

With the successful application and breakthrough of deep learning technology in image segmentation, there has been continuous development in the field of seismic facies interpretation using convolutional neural networks. These intelligent and automated methods significantly reduce manual labor, particularly in the laborious task of manually labeling seismic facies. However, the extensive demand for training data imposes limitations on their wider application. To overcome this challenge, we adopt the UNet architecture as the foundational network structure for seismic facies classification, which has demonstrated effective segmentation results even with small-sample training data. Additionally, we integrate spatial pyramid pooling and dilated convolution modules into the network architecture to enhance the perception of spatial information across a broader range. The seismic facies classification test on the public data from the F3 block verifies the superior performance of our proposed improved network structure in delineating seismic facies boundaries. Comparative analysis against the traditional UNet model reveals that our method achieves more accurate predictive classification results, as evidenced by various evaluation metrics for image segmentation. Obviously, the classification accuracy reaches an impressive 96%. Furthermore, the results of seismic facies classification in the seismic slice dimension provide further confirmation of the superior performance of our proposed method, which accurately defines the range of different seismic facies. This approach holds significant potential for analyzing geological patterns and extracting valuable depositional information.

Monitoring Temperature Profile and Drying Kinetics of Thin-Layer Banana Slices under Controlled Forced Convection Conditions

The drying kinetics of banana slices were examined in a forced convection dryer using an infrared camera to monitor the temperature profile and drying kinetics under control conditions. The air temperature was tested at 40 °C, 50 °C, 60 °C, and 70 °C and the air velocity at 0.2 m/s, 0.5 m/s, and 0.75 m/s, with initial moisture contents of the banana ranging from 76–80% wet basis. The thicknesses of the banana slices being dried were 2, 4, 6, and 8 mm. The optimum drying conditions for the highest drying rate and best color were found to be a temperature of 70 °C, an air velocity of 0.75 m/s, a low relative humidity of 5 to 7%, and banana slices with a thickness of 2 mm. As the air temperature increased, the drying rate and shrinkage also increased. Shrinkage varies concerning moisture loss, and the reduction in radial dimension of banana slices was around 17–23% from the original slice before drying. An empirical mathematical equation was derived by applying the technique of multiple linear regression analysis to the whole dataset of the many experiments of the experimental work. The moisture diffusivity was between 7.88 × 10−10 to 1.04 × 10−10 m2/s, and the average activated energy of the banana was 34.29 kJ/mol. The experimental data were used to fit the drying models. The Midilli model was predicted to produce the closest results to the experimental data.

Maximum velocity projections within 30 seconds: a combination of real-time three-directional flow MRI and cross-sectional volume coverage.

This work is a proof-of-concept realization of a novel technique for rapid volumetric acquisition, reconstruction, and visualization of three-directional (3dir) flow velocities. The technique combines real-time 3dir phase-contrast (PC) flow magnetic resonance imaging (MRI) with real-time cross-sectional volume coverage. It offers a rapid examination without dependence on electrocardiography (ECG) or respiratory gating during a continuous image acquisition at up to 16 fps. Real-time flow MRI utilizes pronounced radial undersampling and a model-based nonlinear inverse reconstruction. Volume coverage is achieved by automatically advancing the slice position of each PC acquisition by a small percentage of the slice thickness. Post-processing involves the calculation of maximum intensity projections along the slice dimension resulting in six direction-selective velocity maps and a maximum speed map. Preliminary applications to healthy subjects at 3 T comprise mapping of the carotid arteries and cranial vessels at 1.0 mm in-plane resolution within 30 s as well as of the aortic arch at 1.6 mm resolution within 20 s. In conclusion, the proposed method for rapid mapping of 3dir flow velocities offers a quick assessment of the vasculature either to provide a first clinical survey or to plan for more detailed studies.

Kz-accelerated variable-density stack-of-stars MRI

This work aimed to develop a modified stack-of-stars golden-angle radial sampling scheme with variable-density acceleration along the slice (kz) dimension (referred to as VD-stack-of-stars) and to test this new sampling trajectory with multi-coil compressed sensing reconstruction for rapid motion-robust 3D liver MRI. VD-stack-of-stars sampling implements additional variable-density undersampling along the kz dimension, so that slice resolution (or volumetric coverage) can be increased without prolonging scan time. The new sampling trajectory (with increased slice resolution) was compared with standard stack-of-stars sampling with fully sampled kz (with standard slice resolution) in both non-contrast-enhanced free-breathing liver MRI and dynamic contrast-enhanced MRI (DCE-MRI) of the liver in volunteers. For both sampling trajectories, respiratory motion was extracted from the acquired radial data, and images were reconstructed using motion-compensated (respiratory-resolved or respiratory-weighted) dynamic radial compressed sensing reconstruction techniques. Qualitative image quality assessment (visual assessment by experienced radiologists) and quantitative analysis (as a metric of image sharpness) were performed to compare images acquired using the new and standard stack-of-stars sampling trajectories. Compared to standard stack-of-stars sampling, both non-contrast-enhanced and DCE liver MR images acquired with VD-stack-of-stars sampling presented improved overall image quality, sharper liver edges and increased hepatic vessel clarity in all image planes. The results have suggested that the proposed VD-stack-of-stars sampling scheme can achieve improved performance (increased slice resolution or volumetric coverage with better image quality) over standard stack-of-stars sampling in free-breathing DCE-MRI without increasing scan time. The reformatted coronal and sagittal images with better slice resolution may provide added clinical value.

Dimensions of slices through the Sierpiński gasket

We discuss the intersections of the d-dimensional Sierpiński gasket with -dimensional hyperplanes in a particular fixed direction. We give the values of the Hausdorff dimension, the lower box dimension, the upper box dimension, and the packing dimension of each slice and determine the criterion for which the Hausdorff dimension of the slice takes Marstrand's value. In order to investigate the slices, we improve the theory of non-autonomous conformal iterated function systems.

Alleviative effect of short-clustered maltodextrin on the quality deterioration of frozen dough: Compared with trehalose and guar gum

The alleviative effect of short-clustered maltodextrin (SCMD) on the quality deterioration of frozen steamed bread dough was investigated in terms of bread characteristics and dough properties with different analytical methods. The results showed that after 56-day frozen storage, SCMD bread had a larger specific volume, lower hardness and looser, more uniform crumb structure compared with Control bread, trehalose (TH) bread and guar gum (GG) bread. Dough viscoelasticity analysis found that the elastic module (G′) of SCMD dough was significantly higher than TH dough but lower than that of GG dough. However, the magnitude of decrease in G′ of GG dough was considerably higher than that of SCMD dough through 56-day frozen storage, which indicated that SCMD could effectively alleviate the damage of long-term frozen storage to gluten. Besides, the gassing rate of SCMD dough, TH dough and GG dough decreased by 15.11%, 20.39% and 23.47% after 56-day frozen storage compared with their respective fresh dough, which indicated the addition of SCMD alleviated the decline of dough gassing rate more effectively. Through SEM analysis, the microstructure of dough after frozen storage was characterized. And the relationships among fractal dimension of bread slices, dough gassing rate and dough elastic module were established for the first time. Finally, analysis of the conformation model further confirmed the possibility of SCMD binding to ice surface by hydrogen-bond interaction, but the MD simulations on binding structures of SCMD-ice complexes need to be further explored.

Slice profile effects on quantitative analysis of hyperpolarized pyruvate.

Magnetic resonance imaging of hyperpolarized pyruvate provides a new imaging biomarker for cancer metabolism, based on the dynamic in vivo conversion of hyperpolarized pyruvate to lactate. Methods for quantification of signal evolution need to be robust and reproducible across a range of experimental conditions. Pharmacokinetic analysis of dynamic spectroscopic imaging data from hyperpolarized pyruvate and its metabolites generally assumes that signal arises from ideal rectangular slice excitation profiles. In this study, we examined whether this assumption could lead to bias in kinetic analysis of hyperpolarized pyruvate and, if so, whether such a bias can be corrected. A Bloch-McConnell simulator was used to generate synthetic data using a known set of "ground truth" pharmacokinetic parameter values. Signal evolution was then analyzed using analysis software that either assumed a uniform slice profile, or incorporated information about the slice profile into the analysis. To correct for slice profile effects, the expected slice profile was subdivided into multiple sub-slices to account for variable excitation angles along the slice dimension. An ensemble of sub-slices was then used to fit the measured signal evolution. A mismatch between slice profiles used for data acquisition and those assumed during kinetic analysis was identified as a source of quantification bias. Results indicate that imperfect slice profiles preferentially increase detected lactate signal, leading to an overestimation of the apparent metabolic exchange rate. The slice profile-correction algorithm was tested in simulation, in phantom measurements, and applied to data acquired from a patient with prostate cancer. The results demonstrated that slice profile-induced biases can be minimized by accounting for the slice profile during pharmacokinetic analysis. This algorithm can be used to correct data from either single or multislice acquisitions.

2D multislice MP2RAGE sequence for fast T1 mapping at 7 T: Application to mouse imaging and MR thermometry.

To develop a 2D radial multislice MP2RAGE sequence for fast and reliable T1 mapping at 7 T in mice and for MR thermometry. The 2D-MP2RAGE sequence was performed with the following parameters: TI1 -TI2 -MP2RAGETR = 1000-3000-9000 ms. The multiple dead times within the sequence were used for interleaved multislice acquisition, enabling one to acquire six slices in 9 seconds. The excitation pulse shape, inversion selectivity, and interslice gap were optimized. In vitro comparison with the inversion-recovery sequence was performed. The T1 variations with temperature were measured on tubes with T1 ranging from 800 ms to 2000 ms. The sequence was used to acquire T1 maps continuously during 30 minutes on the brain and abdomen of healthy mice. A three-lobe cardinal sine excitation pulse, combined with an inversion slice thickness and an interslice gap of respectively 150% and 50% of the imaging slice thickness, led to a SD and bias of the T1 measurements below 1% and 2%, respectively. A linear dependence of T1 with temperature was measured between 10°C and 60°C. In vivo, less than 1% variation was measured between successive T1 maps in the mouse brain. In the abdomen, no obvious in-plane motion artifacts were observed but respiratory motion in the slice dimension led to 6% T1 underestimation. The multislice MP2RAGE sequence could be used for fast whole-body T1 mapping and MR thermometry. Its reconstruction method would enable on-the-fly reconstruction.

A proof of Furstenberg's conjecture on the intersections of $\times p$- and $\times q$-invariant sets

We prove the following conjecture of Furstenberg (1969): if $A,B\subset [0,1]$ are closed and invariant under $\times p \mod 1$ and $\times q \mod 1$, respectively, and if $\log p/\log q\notin \mathbb{Q}$, then for all real numbers $u$ and $v$, $$\dim_{\rm H}(uA+v)\cap B\le \max\{0,\dim_{\rm H}A+\dim_{\rm H}B-1\}.$$ We obtain this result as a consequence of our study on the intersections of incommensurable self-similar sets on $\mathbb{R}$. Our methods also allow us to give upper bounds for dimensions of arbitrary slices of planar self-similar sets satisfying SSC and certain natural irreducible conditions.

Dimension of slices through fractals with initial cubic pattern

In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R n generated from an initial cube pattern with an (n−m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by “multi-rules” take the value in Marstrand’s theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μV is absolutely continuous with respect to the Lebesgue measure L m . When μV ≪ L m , the connection of the local dimension of μV and the box dimension of slices is given.

Efficient multithreading for manycore processor: Multidimensional domain decomposition using Intel® TBB

The Insight Toolkit (ITK) utilizes a generic design for image processing filters that allows many developers to rapidly implement new algorithms. While ITK filters benefit from a platform-independent and versatile multithreading capability, the current implementation does not easily achieve high performance. First, ITK relies on a static decomposition of the image into subsets of equal size which is highly inefficient when the computational complexity varies between subsets (unbalanced workloads). Second, the current domain decomposition is limited to subdivide the input domain along a single dimension (typically the slice dimension in a 3-D volume), which causes a multithreading under-utilization when the number of threads is larger than the size of this dimension when using massively parallel compute systems. We previously presented a new itk::TBBImageToImageFilter class that replaced the static task decomposition by a dynamic task decomposition for improved workload balancing, in which the job scheduling task was optimized using the Intel® Threading Building Blocks (TBB) library. In this work, we propose a new multidimensional dynamic image decomposition approach that allows decomposition over an arbitrary number of dimensions. This new generic multithreading capability, combined with the TBB dynamic task scheduler, substantially improves multithreading performance when using massively parallel processors.

Dual-echo Z-shimmed proton resonance frequency-shift magnetic resonance thermometry near metallic ablation probes: Technique and temperature precision.

To improve the precision of proton resonance frequency-shift magnetic resonance thermometry near ablation probes by recovering near-probe image signals that are typically lost due to magnetic susceptibility-induced field distortions. A dual-echo gradient-recalled echo sequence was implemented, in which the first echo was under- or over-refocused in the slice dimension to recover image signal and temperature precision near a probe, and the second echo was fully refocused to obtain image signal everywhere else in the slice. A penalized maximum likelihood algorithm was implemented to estimate a single temperature map from both echoes. Agar phantom and ex vivo experiments with and without microwave heating at 3 T evaluated how much temperature precision was improved near a microwave ablator compared to a conventional single-echo scan as a function of slice and needle orientation in the magnet. The number of near-probe voxels with temperature standard deviation σ>1°C was decreased by 51% in the phantom experiment, averaged across orientations, and by 31% in the pork. Temperature maps near the probe were more smoother and more complete in all orientations. Dual-echo z-shimmed temperature imaging can recover image signal for more precise temperature mapping near metallic ablation probes. Magn Reson Med 78:2299-2306, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Dimension of slices of Sierpiński-like carpets

We investigate the dimension of intersections of the Sierpiński-like carpets with lines. We show a sufficient condition that for a fixed rational slope the dimension of almost every intersection with respect to the natural measure is strictly greater than s–1 , and almost every intersection with respect to the Lebesgue measure is strictly less than s–1 , where s is the Hausdorff dimension of the carpet. Moreover, we give partial multifractal spectra for the Hausdorff and packing dimension of slices.

Variations of Kähler–Einstein metrics on strongly pseudoconvex domains

Let \((z,s)\in \mathbb {C}^n\times \mathbb {C}^m\) and \(\pi :\mathbb {C}^n\times \mathbb {C}^m\rightarrow \mathbb {C}^m\) be the projection on the second factor. Let \(D\) be a smooth domain in \(\mathbb {C}^{n+m}\) such that for each \(s\in \pi (D)\), the \(n\)-dimensional slice \(D_s=D\cap \pi ^{-1}(s)=\{z:(z,s)\in {D}\}\) is a smooth bounded strongly pseudoconvex domain. By a theorem of Cheng and Yau, for each slice \(D_s\) there exists a unique complete Kahler–Einstein metric \(h_{\alpha \bar{\beta }}(z,s)\) with a negative constant Ricci curvature. We prove that if the slice dimension \(n\) is greater than or equal to \(3\), then \(\log \det (h_{\alpha \bar{\beta }})_{1\le \alpha ,\beta \le {n}}\) is a plurisubharmonic function on \(D\). We also prove that it is a strictly plurisubharmonic function if \(D\) is a strongly pseudoconvex domain.

Measure-theoretic degrees and topological pressure for non-expanding transformations

We consider invariant sets Λ of saddle type, for non-invertible smooth maps f, and equilibrium measures μϕ associated to Hölder potentials ϕ on Λ. We define a notion of measure-theoretic asymptotic degree off|Λ:Λ→Λ, with respect to the measure μϕ on the fractal set Λ. In our case, the equilibrium measure μϕ is the unique linear functional in C(Λ)⁎ tangent to the pressure function P(⋅):C(Λ)→R at ϕ. In particular, for the measure of maximal entropy μ0 of f|Λ, we obtain the asymptotic degree of f|Λ, which represents the average rate of growth of the number of n-preimages of x that remain in Λ when n→∞; notice that, in general, Λ is not totally invariant for f. To this end, we will obtain first a formula for the Jacobians of the probability μϕ, with respect to arbitrary iterates fm, m≥2. We then show that a formula for the topological pressure P(ϕ) that holds in the expanding case, is no longer true on saddle sets. In the saddle case we find a new formula for the pressure, involving weighted sums on preimage sets. We also apply the asymptotic degrees, together with various pressure functionals, in order to obtain estimates for the Hausdorff dimension of stable slices through certain sets of full μϕ-measure in the fractal Λ. In the end, we give also some concrete examples on saddle folded sets.

Shrinkage and porosity effects on heat and mass transfer during potato drying

Fruits and vegetables are porous in nature and undergo pronounced shrinkage during convective drying process. Therefore, shrinkage and porosity should be taken into consideration while predicting heat and mass transfer. This work was conducted to study shrinkage and porosity changes along with simultaneous heat and mass transport during the process. Potato slices were subjected to drying for 7h at 62°C. It was observed that shrinkage varies linearly with respect to moisture content and reduction in radial dimension of potato slices was around 35%. Porosity undergoes rapid increase after attaining certain moisture content in final stages of drying. The work was extended to study the influence of shrinkage and porosity on heat and mass transfer. Simulated results were validated with experimental values. This model can be employed to predict temperature, moisture, density profiles and to study shrinkage and porosity of various fruits and vegetables.

Three‐dimensional Fourier encoding of simultaneously excited slices: Generalized acquisition and reconstruction framework

Simultaneous multislice (SMS) acquisitions have recently received much attention as a means of increasing single-shot imaging speed. SMS acquisitions combine the advantages of single-shot sampling and acceleration along the slice dimension which was previously limited to three-dimensional (3D) volumetric acquisitions. A two-dimensional description of SMS sampling and reconstruction has become established in the literature. Here, we present a more general 3D Fourier encoding and reconstruction formalism for SMS acquisitions that can easily be applied to non-Cartesian SMS acquisitions. An "SMS 3D" k-space is defined in which the field of view along the slice select direction is equal to the number of excited slices times their separation. In this picture, SMS acceleration can be viewed as an undersampling of SMS 3D k-space that can be freely distributed between the in-plane and slice directions as both are effective phase-encoding directions. Use of the SMS 3D k-space picture is demonstrated in phantom and in vivo brain acquisitions including data obtained with blipped-controlled aliasing in parallel imaging sampling. SMS sensitivity encoding reconstruction is demonstrated as well as non-Cartesian SMS imaging using blipped spiral trajectories. The full framework of reconstruction methods can be applied to SMS acquisitions by employing a 3D k-space approach. The blipped-controlled aliasing in parallel imaging method can be viewed as a special case of undersampling an SMS 3D k-space. The extension of SMS methods to non-Cartesian 3D sampling and reconstruction is straightforward.