Spatial Deconvolution Research Articles

Spatial weight matrix in dimensionality reduction reconstruction for micro-electromechanical system-based photoacoustic microscopy

A micro-electromechanical system (MEMS) scanning mirror accelerates the raster scanning of optical-resolution photoacoustic microscopy (OR-PAM). However, the nonlinear tilt angular-voltage characteristic of a MEMS mirror introduces distortion into the maximum back-projection image. Moreover, the size of the airy disk, ultrasonic sensor properties, and thermal effects decrease the resolution. Thus, in this study, we proposed a spatial weight matrix (SWM) with a dimensionality reduction for image reconstruction. The three-layer SWM contains the invariable information of the system, which includes a spatial dependent distortion correction and 3D deconvolution. We employed an ordinal-valued Markov random field and the Harris Stephen algorithm, as well as a modified delay-and-sum method during a time reversal. The results from the experiments and a quantitative analysis demonstrate that images can be effectively reconstructed using an SWM; this is also true for severely distorted images. The index of the mutual information between the reference images and registered images was 70.33 times higher than the initial index, on average. Moreover, the peak signal-to-noise ratio was increased by 17.08% after 3D deconvolution. This accomplishment offers a practical approach to image reconstruction and a promising method to achieve a real-time distortion correction for MEMS-based OR-PAM.

Improved underwater acoustic imaging with non‐uniform spatial resampling RL deconvolution

Underwater acoustic imaging (UAI) can be utilised to observe the spatial distribution of a near-field sound source. The image quality depends on the resolution and sidelobe level of conventional beamforming. The linear array-based UAI can be considered as deconvolution of a two-dimensional point spread function shift-variant model. The performance of UAI can be improved via innovative deconvolution algorithms. In this study, a non-uniform spatial resampling Richardson–Lucy (RL) fast algorithm is designed in which the amount of samples is determined by the power of the UAI output. This allows for a significant decrease in the number of samples compared to the traditional RL algorithm with similar positioning accuracy. Computer simulations and sea trials are performed to validate the effectiveness and feasibility of the proposed method.

Interfacing With Alpha Motor Neurons in Spinal Cord Injury Patients Receiving Trans-spinal Electrical Stimulation.

Trans-spinal direct current stimulation (tsDCS) provides a non-invasive, clinically viable approach to potentially restore physiological neuromuscular function after neurological impairment, e.g., spinal cord injury (SCI). Use of tsDCS has been hampered by the inability of delivering stimulation patterns based on the activity of neural targets responsible to motor function, i.e., α-motor neurons (α-MNs). State of the art modeling and experimental techniques do not provide information about how individual α-MNs respond to electrical fields. This is a major element hindering the development of neuro-modulative technologies highly tailored to an individual patient. For the first time, we propose the use of a signal-based approach to infer tsDCS effects on large α-MNs pools in four incomplete SCI individuals. We employ leg muscles spatial sampling and deconvolution of high-density fiber electrical activity to decode accurate α-MNs discharges across multiple lumbosacral segments during isometric plantar flexion sub-maximal contractions. This is done before, immediately after and 30 min after sub-threshold cathodal stimulation. We deliver sham tsDCS as a control measure. First, we propose a new algorithm for removing compromised information from decomposed α-MNs spike trains, thereby enabling robust decomposition and frequency-domain analysis. Second, we propose the analysis of α-MNs spike trains coherence (i.e., frequency-domain) as an indicator of spinal response to tsDCS. Results showed that α-MNs spike trains coherence analysis sensibly varied across stimulation phases. Coherence analyses results suggested that the common synaptic input to α-MNs pools decreased immediately after cathodal tsDCS with a persistent effect after 30 min. Our proposed non-invasive decoding of individual α-MNs behavior may open up new avenues for the design of real-time closed-loop control applications including both transcutaneous and epidural spinal electrical stimulation where stimulation parameters are adjusted on-the-fly.

Viscoacoustic least-squares migration with a blockwise Hessian matrix: an effective Q approach

Abstract We present an explicit inverse approach using a Hessian matrix for least-squares migration (LSM) with Q compensation. The scheme is developed by incorporating an effective Q-based solution of the viscoacoustic wave equation into a blockwise approximation to the Hessian in LSM, which is implemented after the so-called deabsorption prestack time migration (PSTM). The effective Q model used fully accounts for frequency-dependent traveltime and amplitude at the same imaging location. We can extract the effective Q parameters by scanning during previous deabsorption PSTM. This avoids the challenging task of building the Q model. The blockwise Hessian matrix approach decomposes the full Hessian matrix into a series of computationally tractable small-sized matrices using a localised approach. We derive the explicit formula of the offset-dependent Hessian matrix using an analytical Green's function obtained from deabsorption PSTM. In this way, we can approximate a reflectivity imaging for the targeted zone by a spatial deconvolution of the migrated result with an explicit inverse. The resulting scheme broadens the frequency-band of imaging by deabsorption, and improves the subsurface illumination and spatial resolution through the inverse Hessian. A high-resolution, true-amplitude migrated gather can then be obtained. Synthetic and field data sets demonstrate the proposed blockwise LS-QPSTM.

Spatial deconvolution of aerial radiometric survey and its application to the fallout from a radiological dispersal device

Mapping radioactive contamination using aerial survey measurements is an area under active investigation today. The radiometric aerial survey technique has been extensively applied following reactor accidents and also would provide a key tool for response to a malicious radiological or nuclear incident. Methods exist to calibrate the aerial survey system for quantification of the concentration of natural radionuclides, which can provide guidance. However, these methods have anticipated a spatial distribution of the source which is large in comparison to the survey altitude. In rapid emergency-response aerial surveys of areas of safety concern, deposits of relatively small spatial extent may be expected. The activity of such spatially restricted hot spots is underestimated using the traditional methods. We present here a spatial deconvolution method which can recover some of the variation smoothed out by the averaging due to survey at altitude. We show that the method can recover the true spatial distribution of concentration of a synthetic source. We then apply the method to real aerial survey data collected following detonation of a radiological dispersal device. The findings and implications of the deconvolution are then discussed by reference to a groundbased truckborne survey over the same contamination.

Abstract PR11: Hyperspectral imaging tools capture the spatial organization of cell subsets within the tumor microenvironment

Abstract Immune cells are a major component of the tumor microenvironment (TME). The spatial organization of immune cell subpopulations within the TME is recognized to have biologic significance and clinical relevance. For example, spatial organization of immune cell subsets within the TME is critical for the inhibition of cytotoxic T-cell activity through direct interaction of ligand (PD-L1) with receptor (PD-1)). However, precise spatial deconvolution is limited by the lack of imaging algorithms for in situ multiplex single cell analyses as flow cytometry does not preserve data in the spatial dimension. To this end, we have developed a hyperspectral imaging platform designed for analyzing multichannel immunohistochemical-stained tissue sections for generating cell density data and reconstructing spatial architecture for tumor biology as well as clinical association studies. Whole-tissue sections from 20 lung adenocarcinomas with at least 5 years’ follow-up were stained for CD3 (pan-T cell), CD8 (cytotoxic T cell), and CD79a (B cell and plasma cell) and counterstained with hematoxylin. Multispectral images were acquired for five fields of view and analyzed to quantify cell types. Regions of Interest (ROIs) were then identified and analyzed in order to quantify cell-cell spatial relationships. Nonrandom patterns of immune cell distributions were identified using the Monte Carlo resampling method (500 iterations). Cell counts, densities, spatial relationships, and significant immune cell distributions were associated with clinical features (Kruskal-Wallis p<0.001). Our analysis generated 234 image files for analysis, with an average of 16,400 cells per image. The densities of intratumoral CD8+ cytotoxic T cells were significantly higher in nonrecurrent cases, agreeing with literature reports. Similarly, cell sociology deductions identified relationships associated with metastasis: tumor cells in nonmetastatic cases had increased numbers of CD8+ cytotoxic T-cell neighbors. Following Monte Carlo analysis, nonrandom cell~cell spatial proximities emerged that were not identified at a cell density level. We have developed a hyperspectral imaging platform capable of quantifying cell-cell spatial relationships within tissue sections. This technology can be applied to larger clinical cohorts for the study of therapeutically targetable immune cell subsets with the goal of identifying patterns that correlate with clinical response and patient outcome. This abstract is also being presented as Poster B16. Citation Format: Katey S.S. Enfield, Spencer D. Martin, Sonia H.Y. Kung, Paul Gallagher, Calum E. MacAulay, Martial Guillaud, Wan L. Lam. Hyperspectral imaging tools capture the spatial organization of cell subsets within the tumor microenvironment [abstract]. In: Proceedings of the Fifth AACR-IASLC International Joint Conference: Lung Cancer Translational Science from the Bench to the Clinic; Jan 8-11, 2018; San Diego, CA. Philadelphia (PA): AACR; Clin Cancer Res 2018;24(17_Suppl):Abstract nr PR11.

Assisted seismic history matching of the Nelson field: Managing large numbers of unknowns by divide and conquer

Automatic history matching may be used to condition reservoir simulation models with time-lapse seismic data. Stochastic optimization algorithms are used to perform a good search of the parameter space to ensure effective determination of the best models. These approaches can require many thousands of simulations for large dimensional problems. Divide and conquer is an assisted history matching approach that enables deconvolution of the parameters so that they can be searched more efficiently and also leads to better uncertainty analysis.We present an application of this approach on the Nelson field. Nine years of production history data are used along with baseline and monitor seismic surveys. Localised variations were made to permeability and net-to-gross ratio in the model. The reservoir was divided into separate parameter regions by combining experimental design and proxy model analysis. The former enabled insignificant parameters to be discarded while the latter showed that each region could be treated as a separate history matching sub-problem. Each sub-problem was then solved simultaneously using an adapted stochastic neighbourhood algorithm.The results show that a forty-two dimensional problem could be reduced to a combination of three 9D problems and a 3D problem due to the spatial deconvolution of parameters and misfits. An improved match was obtained for the production and seismic data. Compared to a full stochastic search of the parameter space, the number of required models was several orders of magnitude smaller. Improved uncertainty analysis was made possible resulting in better understanding of the future behaviour of the reservoir.An improved match to reservoir models leads to better confidence in their prediction and thus they can be used more effectively in reservoir management. The method presented here to improve the match retains the benefits of stochastic searching without the penalty of requiring an impractical number of simulations.

Her2Net: A Deep Framework for Semantic Segmentation and Classification of Cell Membranes and Nuclei in Breast Cancer Evaluation.

We present an efficient deep learning framework for identifying, segmenting, and classifying cell membranes and nuclei from human epidermal growth factor receptor-2 (HER2)-stained breast cancer images with minimal user intervention. This is a long-standing issue for pathologists because the manual quantification of HER2 is error-prone, costly, and time-consuming. Hence, we propose a deep learning-based HER2 deep neural network (Her2Net) to solve this issue. The convolutional and deconvolutional parts of the proposed Her2Net framework consisted mainly of multiple convolution layers, max-pooling layers, spatial pyramid pooling layers, deconvolution layers, up-sampling layers, and trapezoidal long short-term memory (TLSTM). A fully connected layer and a softmax layer were also used for classification and error estimation. Finally, HER2 scores were calculated based on the classification results. The main contribution of our proposed Her2Net framework includes the implementation of TLSTM and a deep learning framework for cell membrane and nucleus detection, segmentation, and classification and HER2 scoring. Our proposed Her2Net achieved 96.64% precision, 96.79% recall, 96.71% F-score, 93.08% negative predictive value, 98.33% accuracy, and a 6.84% false-positive rate. Our results demonstrate the high accuracy and wide applicability of the proposed Her2Net in the context of HER2 scoring for breast cancer evaluation.

Cortical depth profiles of luminance contrast responses in human V1 and V2 using 7 T fMRI.

Neural activity in early visual cortex is modulated by luminance contrast. Cortical depth (i.e., laminar) contrast responses have been studied in monkey early visual cortex, but not in humans. In addition to the high spatial resolution needed and the ensuing low signal-to-noise ratio, laminar studies in humans using fMRI are hampered by the strong venous vascular weighting of the fMRI signal. In this study, we measured luminance contrast responses in human V1 and V2 with high-resolution fMRI at 7 T. To account for the effect of intracortical ascending veins, we applied a novel spatial deconvolution model to the fMRI depth profiles. Before spatial deconvolution, the contrast response in V1 showed a slight local maximum at mid cortical depth, whereas V2 exhibited a monotonic signal increase toward the cortical surface. After applying the deconvolution, both V1 and V2 showed a pronounced local maximum at mid cortical depth, with an additional peak in deep grey matter, especially in V1. Moreover, we found a difference in contrast sensitivity between V1 and V2, but no evidence for variations in contrast sensitivity as a function of cortical depth. These findings are in agreement with results obtained in nonhuman primates, but further research will be needed to validate the spatial deconvolution approach.

In Vivo Neuromechanics: Decoding Causal Motor Neuron Behavior with Resulting Musculoskeletal Function

Human motor function emerges from the interaction between the neuromuscular and the musculoskeletal systems. Despite the knowledge of the mechanisms underlying neural and mechanical functions, there is no relevant understanding of the neuro-mechanical interplay in the neuro-musculo-skeletal system. This currently represents the major challenge to the understanding of human movement. We address this challenge by proposing a paradigm for investigating spinal motor neuron contribution to skeletal joint mechanical function in the intact human in vivo. We employ multi-muscle spatial sampling and deconvolution of high-density fiber electrical activity to decode accurate α-motor neuron discharges across five lumbosacral segments in the human spinal cord. We use complete α-motor neuron discharge series to drive forward subject-specific models of the musculoskeletal system in open-loop with no corrective feedback. We perform validation tests where mechanical moments are estimated with no knowledge of reference data over unseen conditions. This enables accurate blinded estimation of ankle function purely from motor neuron information. Remarkably, this enables observing causal associations between spinal motor neuron activity and joint moment control. We provide a new class of neural data-driven musculoskeletal modeling formulations for bridging between movement neural and mechanical levels in vivo with implications for understanding motor physiology, pathology, and recovery.

Driven by excess? Climatic implications of new global mapping of near-surface water-equivalent hydrogen on Mars

We present improved Mars Odyssey Neutron Spectrometer (MONS) maps of near-surface Water-Equivalent Hydrogen (WEH) on Mars that have intriguing implications for the global distribution of “excess” ice, which occurs when the mass fraction of water ice exceeds the threshold amount needed to saturate the pore volume in normal soils. We have refined the crossover technique of Feldman et al. (2011) by using spatial deconvolution and Gaussian weighting to create the first globally self-consistent map of WEH. At low latitudes, our new maps indicate that WEH exceeds 15% in several near-equatorial regions, such as Arabia Terra, which has important implications for the types of hydrated minerals present at low latitudes. At high latitudes, we demonstrate that the disparate MONS and Phoenix Robotic Arm (RA) observations of near surface WEH can be reconciled by a three-layer model incorporating dry soil over fully saturated pore ice over pure excess ice: such a three-layer model can also potentially explain the strong anticorrelation of subsurface ice content and ice table depth observed at high latitudes. At moderate latitudes, we show that the distribution of recently formed impact craters is also consistent with our latest MONS results, as both the shallowest ice-exposing crater and deepest non-ice-exposing crater at each impact site are in good agreement with our predictions of near-surface WEH. Overall, we find that our new mapping is consistent with the widespread presence at mid-to-high Martian latitudes of recently deposited shallow excess ice reservoirs that are not yet in equilibrium with the atmosphere.

Light sheet luminescence imaging with Cherenkov excitation in thick scattering media.

Light scattering leads to a severe loss of axial and transverse resolution with depth into tissue, limiting accuracy and value of biomedical luminescence imaging techniques. High-resolution imaging beyond a few-millimeter depth is prohibited because diffusive transport dominates beyond a few scattering distances. In this study, light sheet imaging through scattering media is demonstrated using a radiotherapy linear accelerator to deliver well-defined thin scanned sheets of x-rays. These sheets produce Cherenkov light within the medium, which in turn excites luminescence of an optical probe across the sheet plane. This luminescence can then be imaged by an intensified camera positioned perpendicular to the sheet plane. The precise knowledge of the light sheet position within the medium allowed for efficient attenuation correction of the signal with depth as well as spatial deconvolution of the excitation light. Together these methods allowed for the first time, to the best of our knowledge, high-resolution imaging of tissue-equivalent phantoms up to 3 cm thick, yielding the precise position and shape of luminescent lesions located deep in tissue without the need for nonlinear image reconstruction.

Analysis of a spatially deconvolved solar pore

Solar pores are active regions with large magnetic field strengths and apparent simple magnetic configurations. Their properties resemble the ones found for the sunspot umbra although pores do not show penumbra. Therefore, solar pores present themselves as an intriguing phenomenon that is not completely understood. We examine in this work a solar pore observed with Hinode/SP using two state of the art techniques. The first one is the spatial deconvolution of the spectropolarimetric data that allows removing the stray light contamination induced by the spatial point spread function of the telescope. The second one is the inversion of the Stokes profiles assuming local thermodynamic equilibrium that let us to infer the atmospheric physical parameters. After applying these techniques, we found that the spatial deconvolution method does not introduce artefacts, even at the edges of the magnetic structure, where large horizontal gradients are detected on the atmospheric parameters. Moreover, we also describe the physical properties of the magnetic structure at different heights finding that, in the inner part of the solar pore, the temperature is lower than outside, the magnetic field strength is larger than 2 kG and unipolar, and the LOS velocity is almost null. At neighbouring pixels, we found low magnetic field strengths of same polarity and strong downward motions that only occur at the low photosphere, below the continuum optical depth $\log \tau=-1$. Finally, we studied the spatial relation between different atmospheric parameters at different heights corroborating the physical properties described before.

Complex modes of bonding: NCI/ELI-D vs. DORI surface analyses of hapticities and hydrogen–hydrogen contacts in zincocene related compounds

Atoms-in-molecules (AIM) topology is prone to wrong/ambiguous bond assignments (lacking bond critical points) in areas of low electron densities (ED), e.g. for hydrogen–hydrogen contacts, and flat density gradients, e.g. for metal–ring contacts (hapticities), both in experimental and computed ED. Within this study, two ED-derived bonding indicators are applied to a set of zincocene related compounds: non-covalent interactions (NCI) surfaces are combined with electron localizability indicator (ELI-D) surfaces and compared to density overlap regions indicator (DORI) surfaces. Both methods (NCI/ELI-D, DORI) result in spatial deconvolution of covalent and non-covalent interactions and unravel weak interactions not observed in the AIM topology.

Analysis of horizontal flows in the solar granulation

Solar limb observations sometimes reveal the presence of a satellite lobe in the blue wing of the Stokes I profile from pixels belonging to granules. The presence of this satellite lobe has been associated in the past to strong line of sight gradients and, as the line of sight component is almost parallel to the solar surface, to horizontal granular flows. We aim to increase the knowledge about these horizontal flows studying a spectropolarimetric observation of the north solar pole. We will make use of two state of the art techniques, the spatial deconvolution procedure that increases the quality of the data removing the stray light contamination, and spectropolarimetric inversions that will provide the vertical stratification of the atmospheric physical parameters where the observed spectral lines form. We inverted the Stokes profiles using a two component configuration, obtaining that one component is strongly blueshifted and displays a temperature enhancement at upper photospheric layers while the second component has low redshifted velocities and it is cool at upper layers. In addition, we examined a large number of cases located at different heliocentric angles, finding smaller velocities as we move from the centre to the edge of the granule. Moreover, the height location of the enhancement on the temperature stratification of the blueshifted component also evolves with the spatial location on the granule being positioned on lower heights as we move to the periphery of the granular structure.

Spatial deconvolution of spectropolarimetric data: an application to quiet Sun magnetic elements

Observations of the Sun from the Earth are always limited by the presence of the atmosphere, which strongly disturbs the images. A solution to this problem is to place the telescopes in space satellites, which produce observations without any (or limited) atmospheric aberrations. However, even though the images from space are not affected by atmospheric seeing, the optical properties of the instruments still limit the observations. In the case of diffraction limited observations, the PSF establishes the maximum allowed spatial resolution, defined as the distance between two nearby structures that can be properly distinguished. In addition, the shape of the PSF induce a dispersion of the light from different parts of the image, leading to what is commonly termed as stray light or dispersed light. This effect produces that light observed in a spatial location at the focal plane is a combination of the light emitted in the object at relatively distant spatial locations. We aim to correct the effect produced by the telescope's PSF using a deconvolution method, and we decided to apply the code on Hinode/SP quiet Sun observations. We analyze the validity of the deconvolution process with noisy data and we infer the physical properties of quiet Sun magnetic elements after the deconvolution process.

A hot bubble at the centre of M 81

Context. Messier 81 has the nearest active nucleus with broad H$\alpha$ emission. A detailed study of this galaxy's centre is important for understanding the innermost structure of the AGN phenomenon. Aims. Our goal is to seek previously undetected structures using additional techniques to reanalyse a data cube obtained with the GMOS-IFU installed on the Gemini North telescope (Schnorr M\"uller et al. 2011). Method. We analysed the data cube using techniques of noise reduction, spatial deconvolution, starlight subtraction, PCA tomography, and comparison with HST images. Results. We identified a hot bubble with T $>$ 43500 K that is associated with strong emission of [N II]$\lambda$5755\AA\ and a high [O I]$\lambda$6300/H$\alpha$ ratio; the bubble displays a bluish continuum, surrounded by a thin shell of H$\alpha$ + [N II] emission. We also reinterpret the outflow found by Schnorr M\"uller et al. (2011) showing that the blueshifted cone nearly coincides with the radio jet, as expected. Conclusions. We interpret the hot bubble as having been caused by post starburst events that left one or more clusters of young stars, similar to the ones found at the centre of the Milky Way, such as the Arches and the IRS 16 clusters. Shocked structures from combined young stellar winds or supernova remnants are probably the cause of this hot gas and the low ionization emission.

The roles of the spatial regularization in seismic deconvolution

In this paper we investigate the roles of the spatial regularization in seismic deconvolution. The spatial regularization is described as a L2 norm of the lateral reflectivity difference imposed on multi-trace data misfit term. In essence, the spatial regularization acts as a band-pass filter along the spatial direction. Therefore, it can suppress the high-wavenumber components of the estimated reflectivity, for example, noisy trails like noodles which usually caused by temporal regularized deconvolution. As well, the spatial regularization can help recovering the reflectivity of discarding traces by repeatedly and linearly weighting its neighboring reflectivity, thereby exploring the spatial continuities among traces. Moreover, the spatial regularization can help stabilizing inversion, just like the temporal regularization. Both synthetic and field data examples are used to demonstrate the three roles of the spatial regularization by comparing spatial regularized deconvolution with conventional temporal deconvolution implemented by minimizing a data misfit and a L2 norm or a L1 norm of reflectivity. Furthermore, the synthetic examples also clearly illustrate that the spatial regularization can help yielding a high resolution and meanwhile high signal-to-noise ratio deconvolution result, which matches best with the reference reflectivity.

Retrieving surface waves from ambient seismic noise using seismic interferometry by multidimensional deconvolution

AbstractRetrieving virtual source surface waves from ambient seismic noise by cross correlation assumes, among others, that the noise field is equipartitioned and the medium is lossless. Violation of these assumptions reduces the accuracy of the retrieved waves. A point‐spread function computed from the same ambient noise quantifies the associated virtual source's spatial and temporal smearing. Multidimensional deconvolution (MDD) of the retrieved surface waves by this function has been shown to improve the virtual source's focusing and the accuracy of the retrieved waves using synthetic data. We tested MDD on data recorded during the Batholiths experiment, a passive deployment of broadband seismic sensors in British Columbia, Canada. The array consisted of two approximately linear station lines. Using 4 months of recordings, we retrieved fundamental‐mode Rayleigh waves (0.05–0.27 Hz). We only used noise time windows dominated by waves that traverse the northern line before reaching the southern (2.5% of all data). Compared to the conventional cross‐correlation result based on this subset, the MDD waveforms are better localized and have significantly higher signal‐to‐noise ratio. Furthermore, MDD corrects the phase, and the spatial deconvolution fills in a spectral (f, k domain) gap between the single‐frequency and double‐frequency microseism bands. Frequency whitening of the noise also fills the gap in the cross‐correlation result, but the signal‐to‐noise ratio of the MDD result remains higher. Comparison of the extracted phase velocities shows some differences between the methods, also when all data are included in the conventional cross correlation.

Edge impurity rotation profile measurement by using high-resolution ultraviolet/visible spectrometer on J-TEXT.

An upgrade of the edge rotation diagnostic system is achieved by increasing the number of viewing channels to 17 on J-TEXT tokamak. With the upgrade, the spatial resolution reaches 1 cm. The bulk plasma is used as the calibration light source. And the toroidal velocity profile of C V (carbon V) at edge region is obtained by using a spatial deconvolution technique. The valid measurement region is at ρ = 0.6-0.9, corresponding to the emitting region of C V. The preliminary experimental results express that the velocity of plasma may have a zero point near ρ = 0.85.