Spherical Volume Research Articles

Time-course assessment of 3D-image distortion on the 1.5 T Marlin/Elekta Unity MR-LINAC

PurposeThe efficacy of MR-guided radiotherapy on a MR-LINAC (MR-L) is dependent on the geometric accuracy of its MR images over clinically relevant Fields-of-View (FOVs). Our objectives were to: evaluate gradient non-linearity (GNL) on the Elekta Unity MR-L across time via 76 weekly measurements of 3D-distortion over concentrically larger diameter spherical volumes (DSVs); quantify distortion measurement error; and assess the temporal stability of spatial distortion using statistical process control (SPC). MethodsMR-image distortion was assessed using a large-FOV 3D-phantom containing 1932 markers embedded in seven parallel plates, spaced 25 mm × 25 mm in- and 55 mm through-plane. Automatically analyzed T1 images yielded distortions in 200, 300, 400 and 500 mm concentric DSVs. Distortion measurement error was evaluated using median absolute difference analysis of imaging repeatability tests. ResultsOver the measurement period absolute time-averaged distortion varied between: dr = 0.30 – 0.49 mm, 0.53 – 0.80 mm, 1.0 – 1.4 mm and 2.28 – 2.37 mm, for DSVs 200, 300, 400 and 500 mm at the 98th percentile level. Repeatability tests showed that imaging/repositioning introduces negligible error: mean ≤ 0.02 mm (max ≤ 0.3 mm). SPC analysis showed image distortion was stable across all DSVs; however, noticeable changes in GNL were observed following servicing at the one-year mark. ConclusionsImage distortion on the MR-L is in the sub-millimeter range for DSVs ≤ 300 mm and stable across time, with SPC analysis indicating all measurements remain within control for each DSV.

Molecular dynamics simulation of bulk nanobubbles

The long-term stability of nanobubbles with high internal gas pressure is a puzzling question for nanobubble researchers. The classical Molecular Dynamics simulation based on LAMMPS software was used to evaluate the performance of an oxygen nanobubble with high gas density. This research consists of two main cases. In the first case, bubble behavior was examined with 3247 O2 molecules embedded in a 4.5 nm radius spherical volume to represent the bubble and was surrounded by 438,490 H2O molecules with 1 g/cm3 density. In the second case, the parametric study was conducted while maintaining the same parameters where the amount of O2 molecules changed at the initial configuration. Hence six different O2 bubble configurations were simulated under two different temperature settings, 20 ℃ and 30 ℃. The Lennard Jones potentials are used for molecular interactions. The simulations were run first under the NVT and then changed to the NPT ensemble. Simulation results were analyzed for bubble size, pressure, surface tension, gas diffusion, the influence of internal initial gas densities, gas concentration, and temperature conditions. The high initial gas concentration with high initial internal gas density causes a more stable bubble condition under both NVT and NPT ensembles. This stability can be attributed to the gas supersaturation conditions. The systems with low initial internal gas densities transferred to a smaller radius gas cluster with a high internal density as they shifted to the NPT ensemble. The system with a higher temperature causes elevated system pressures at NVT and volume expansion during NPT. Under NVT simulation, bubble size was higher at lower temperatures. Under NPT conditions, bubble size increases for larger initial density cases and decreases for lower density cases. Further increased temperature causes faster gas diffusion, and higher internal bubble pressure leads to unstable conditions.

Magnetic, Mechanical and Thermal Modeling of Superconducting, Whole-body, Actively Shielded, 3 T MRI Magnets Wound Using MgB2 Strands for Liquid Cryogen Free Operation.

we present magnetic, mechanical and thermal modeling results for a 3 Tesla actively shielded whole body MRI (Magnetic Resonance Imaging) magnet consisting of coils with a square cross section of their windings. The magnet design was a segmented coil type optimized to minimize conductor length while hitting the standard field quality and DSV (Diameter of Spherical Volume) specifications as well as a standard, compact size 3 T system. It had an overall magnet length and conductor length which can lead to conduction cooled designs comparable to NbTi helium bath cooled 3 T MRI magnets. The design had a magnetic field homogeneity better than 10 ppm (part-per-million) within a DSV (Diameter of Spherical Volume) of 48 cm and the total magnet winding length of 1.37 m. A new class of MgB2 strand especially designed for MRI applications was considered as a possible candidate for winding such magnets. This work represents the first magnetic, mechanical and thermal design for a whole-body 3 T MgB2 short (1.37 m length) MRI magnet based on the performance parameters of existing MgB2 wire. 3 Tesla MRI magnet can operate at 20 K at 67 % of its critical current.

Gravitational Collision of Small Nonspherical Particles: Swept Volumes of Prolate and Oblate Spheroids in Calm Air

Abstract The aggregation rate of ice crystals depends on their shape and intercrystal relative velocity. Unlike spherical particles, the nonspherical ones can have various orientations relative to the gravitational force in the vertical direction and can approach each other at many different angles. Furthermore, the fall velocity of such particles could deviate from the vertical direction velocity. These properties add to the computational complexity of nonspherical particle collisions. In this study, we derive general mathematical expressions for gravity-induced swept volumes of spheroidal particles. The swept volumes are shown to depend on the particles’ joint orientation distribution and relative velocities. Assuming that the particles are Stokesian prolate and oblate spheroids of different sizes and aspect ratios, the swept volumes were calculated and compared to those of equivalent volume spheres. Most calculated swept volumes were larger than the swept volumes of equivalent spherical particles, sometimes by several orders of magnitude. This was due to both the complex geometry and the side drift, experienced by spheroids falling with their major axes not parallel to gravity. We expect that the collision rate between nonspherical particles is substantially higher than that of equivalent volume spheres because the collision process is nonlinear. These results suggest that the simplistic approach of equivalent spheres might lead to serious errors in the computation of the collision rate.

Development of Electron Paramagnetic Resonance Magnet System for In Vivo Tooth Dosimetry

As part of a homebuilt continuous wave electron paramagnetic resonance (EPR) spectrometer operating at 1.2 GHz, a magnet system for in vivo tooth dosimetry was developed. The magnet was designed by adopting NdFeB permanent magnet (PM) for the main magnetic field generation. For each pole of the magnet, 32 cylindrical PMs were arranged in 2 axially aligned ring arrays. The pole gap was 18 cm, which was wide enough for a human head breadth. The measured magnetic field was compared with the magnetic field distribution calculated in a finite element method (FEM) simulation. EPR spectra of intact human teeth irradiated 5 and 30 Gy were measured for the performance test with the developed magnet system and spectrometer. The measured mean magnetic flux density was estimated to be 44.45 mT with homogeneity of 1,600 ppm in a 2 cm diameter of the spherical volume of the XY plane, which was comparable to the FEM simulation results. The sweep coefficient of the magnetic field sweep coil was 0.35 mT per Ampere in both the measurement and FEM simulation. With ±9 A current, the sweep range was 5.7 mT, which was sufficiently wide to measure the tooth radiation-induced signal (RIS) and reference material. The peak-to-peak amplitude of the measured modulation field was 0.38 mT at the center of the magnet. With the developed magnet fully integrated into an EPR system, the EPR spectra of 5 and 30 Gy irradiated teeth were successfully acquired. The developed magnet system showed sufficiently acceptable performance in terms of magnetic flux density and homogeneity. The EPR spectrum of tooth RIS could be measured ex vivo. The RIS of 5 and 30 Gy irradiated teeth was clearly distinguishable from intact human teeth.

Research on the interface and properties of spherical ZTA particles reinforced Fe-Cr-B matrix composite

Spherical zirconia toughened alumina (ZTA) particles reinforced Fe–Cr–B matrix composite was prepared by the liquid phase sintering in the current study. The results demonstrated that at the sintering temperature of 1380 °C, a prominent interface layer was formed between the spherical ZTA particles and the Fe–Cr–B alloy, the thickness of which is about 50 μm. The combined effects of B element, Mn element and SiO2 promote the formation of the interface. Mn2SiO4, Fe2SiO4, MnFe2O4 and B2O3 were formed at the interface. The formation mechanism is described. Hardness and Young's modulus of SZ40 sample at the interface are 12.88 and 146.60 GPa, respectively, which play a crucial role in combining of ZTA particles and the matrix. The wear resistance of the composite prepared in the current study is excellent. The wear volume loss decreases gradually with the increase of spherical ZTA volume fraction. Under the same wear conditions, the volume loss of the SZ40sample is only 9.65% of that of the Cr16 sample and is 14.33% of that of the matrix sample. The spherical ZTA in the composite is higher than the Fe–Cr–B matrix, forming a “shadow effect” to protect the matrix. The Fe–Cr–B matrix has better toughness and can support the spherical ZTA particles during the wear process. Effective combination of the advantages of the two reduces the volume loss of the composite.

The microstructure characterization and elastic properties of closed-cell foams

The present study investigated the microstructure and compressive response of ALPORAS closed-cell foam. The micro-CT technique was adopted to study the interior structure of the foam. Image processing algorithms were then incorporated to measure the geometrical characteristics of the foam cellular microstructure, including the size, surface area, geometrical shape, aspect ratio, and sphericity of cells. The cells were irregular polyhedra with approximately 14–15 faces and 5 edges per face; they had longer dimensions in the gravitational direction than in the other two mutually orthogonal directions. Three statistical measurements were employed in the development of random 3D numerical models based on the Laguerre tessellation of random close packed spheres along with three probability density functions for sphere size distributions. The effects of parameters such as probability density functions, sphere volume fraction, and coefficient of variation in sphere volume on the geometrical characteristics of the developed numerical models were examined. The difference in geometric characteristics of the numerical models generated using different probability functions was nonsignificant. Numerical simulations were subsequently conducted using the developed numerical models. The comparison between numerical and experimental results revealed that numerical models overestimated the experimental value by a factor of approximately 3. This discrepancy can be attributed to the difference in detailed microstructural features between the generated numerical models and real foam.

QCD phase diagram in a finite volume in the PNJL model

Abstract In this work, we study the quantum chromodynamics phase diagram at finite temperature and non-zero chemical potential in the framework of the SU(2) flavor of the Polyakov–Nambu – Jona–Lasinio model (PNJL). Applying multiple reflection expansion to cubic and spherical finite volumes of different sizes and boundary conditions, the chiral phase transition and deconfinement of strongly interacting matter are analyzed. We give special attention to find and locate the critical endpoint and locating the critical endpoint, if it exists, as a function of the volume size and its shape, and its dependence of chemical potential and temperature.

On the Geometric Sensitivity of the EEG Inversion Algorithm

Electroencephalography (EEG) is a noninvasive method of brain imaging. In particular, the inverse EEG problem consists of identifying the electrical activity inside the brain from measurements of the electric potential on the scalp. Since the mathematics of EEG are modeled by a linear boundary value problem with sources which are distributed electric dipoles, it follows that the main effort is focused in the problem of identifying the location and the moment of a single dipole from recorded EEG data. In medical practice the developed algorithms for this problem are based on the assumption that the brain is a sphere. However, the realistic model of the shape of the brain is that of an ellipsoid. Consequently, that generates an error on the medical practice due to the interpretation of the data, which are obtained on an ellipsoidal figure and are processed as they were obtained on a sphere. The present work provides an analysis of this problem and proves that for moderate values of the principal eccentricities of the ellipsoid the error remains insignificant, while as the values of the eccentricities increase the error becomes large. The comparison is between a realistic ellipsoid and a sphere of equal volume. In fact, discrepancies higher than 20% are found when the maximum eccentricity of the ellipsoid becomes larger than 0.9. Fortunately, the principal eccentricities of the human brain are within the region of insignificant errors and therefore the credibility of the medical practice is saved.

Comparative study on HTS magnet coil design approach for 1.0 T @ 65 K with 10 ppm field homogeneity at 80 mm DSV

A comparative study is carried out between two distinct coil design approaches (Multi-coil and Compensated solenoid) for the development of 1.0 T REBCO main magnet coil suitable for Extremity Magnetic Resonance Imaging (E-MRI). The design includes a operating temperature of 65 K, for the enhancement of Ic with field anisotropy of REBCO tape. Each magnet design consists of HTS tape wound in the form of double pancake coils, having the inner winding diameter as 200 mm, whereas both outer diameter and magnet length are restricted to less than 400 mm. The two coils configurations are compared by keeping the bore inner diameter, outer diameter, length and fixed HTS tape length constant. Thereafter the parameters such as peak flux density, maximum radial field, stray field distribution, coil stress and field homogeneity for 80 mm diameter of spherical volume (DSV) are analyzed. Multi-coil design gives a better field homogeneity (315 ppm) as compared to Compensated solenoid.

Open magnetic shielding for static and alternating field.

To meet the increasing and various demands for low magnetic field measurement, an open magnetic shielding system created using a combination of copper coils and precisely designed superconducting closed coils is proposed. After testing, the prototype system showed a shielding factor of more than 10 000 in the direct current field and most importantly, a shielding factor of at least 100 in the alternating field from frequencies of 0.01-100Hz in a 5cm spherical volume. We interestingly found that the magnetic purity of the open system is capable of catching up with the magnetically shielded room with moderate performance. The structure and principle of the system are introduced in this paper. A key factor that makes the system possible is the decoupled interaction between the copper coils and superconducting coils. The limitations of this system and ways to improve its performance are discussed. This novel approach provides a more sophisticated and flexible way to achieve open magnetic shielding.

Design and test of an open portable MRI system

PurposeThe purpose of this paper is the design study and realisation of portable low-field open MRI system.Design/methodology/approachThe design of the magnetic resonance imaging (MRI) system is based on an optimization study using a genetic algorithm. Non-linear two-dimensional and three-dimensional numerical electromagnetic models are developed and inserted in the optimization environment.FindingsThe results are found to be consistent with those issued from fully experimental tests. The static field produced by the device is 0.295 T with a homogeneity of 2.8% (28,000 ppm) over 100 mm diameter sphere volume. The z-axis gradient coils are capable of generating switching gradients with an amplitude of 8 mT/m and a frequency of 1.2 kHz.Originality/valueOur system is an open portable MRI which can be used in an ambulance. The open topology permits an easy access into the lateral sides when a surgery using surgical instrument with video feedback is needed.

On the evaluation of the intrinsic stability of indium-nanoparticulate organic matter complexes

HypothesisProper evaluation of the intrinsic stability of metal complexes with humic nanoparticles calls for a robust representation of the particulate electrostatic features. Addressing here the case of trivalent metal association with humics for which a significant electrostatic contribution is expected, we report a robust interpretative approach as an alternative to the conventional but approximative Donnan model applied in popular speciation codes. ExperimentsThe intrinsic chemical binding affinity of Indium to humic nanoparticles is addressed from equilibrium electroanalytical measurements (Absence of Gradient and Nernstian Equilibrium Stripping) in NaClO4 electrolyte (10–100 mM, pH4) at different metal-to-humics concentration ratios. The electrostatic contribution was evaluated using a Poisson-Boltzmann based-approach where the key electrostatic descriptors of humics are involved. FindingsThe electrochemical results interpreted in the light of so identified non-specific indium binding contribution evidences a dramatic impact of electrostatics on indium complexation by humics, with e.g. in 10 mM electrolyte an intraparticulate Boltzmann metal accumulation factor that is ca. 5 times larger than that reported for cadmium and highly-charged fulvics complexants. A successful comparison between theory and experiments is consistently achieved over the tested electrolyte concentrations with the only adjustment of the radius of the metal accumulation spherical volume. The analysis reveals the necessity to consider full equilibration of charged humics with its intraparticulate counterion atmosphere.

Longitudinal assessment of quality assurance measurements in a 1.5T MR-linac: Part II-Magnetic resonance imaging.

PurposeTo describe and report longitudinal quality assurance (QA) measurements for the magnetic resonance imaging (MRI) component of the Elekta Unity MR‐linac during the first year of clinical use in our institution.Materials and methodsThe performance of the MRI component of Unity was evaluated with daily, weekly, monthly, and annual QA testing. The measurements monitor image uniformity, signal‐to‐noise ratio (SNR), resolution/detectability, slice position/thickness, linearity, central frequency, and geometric accuracy. In anticipation of routine use of quantitative imaging (qMRI), we characterize B0/B1 uniformity and the bias/reproducibility of longitudinal/transverse relaxation times (T1/T2) and apparent diffusion coefficient (ADC). Tolerance levels for QA measurements of qMRI biomarkers are derived from weekly monitoring of T1, T2, and ADC.ResultsThe 1‐year assessment of QA measurements shows that daily variations in each MR quality metric are well below the threshold for failure. Routine testing procedures can reproducibly identify machine issues. The longitudinal three‐dimensional (3D) geometric analysis reveals that the maximum distortion in a diameter of spherical volume (DSV) of 20, 30, 40, and 50 cm is 0.4, 0.6, 1.0, and 3.1 mm, respectively. The main source of distortion is gradient nonlinearity. Maximum peak‐to‐peak B0 inhomogeneity is 3.05 ppm, with gantry induced B0 inhomogeneities an order of magnitude smaller. The average deviation from the nominal B1 is within 2%, with minimal dependence on gantry angle. Mean ADC, T1, and T2 values are measured with high reproducibility. The median coefficient of variation for ADC, T1, and T2 is 1.3%, 1.1%, and 0.5%, respectively. The median bias for ADC, T1, and T2 is −0.8%, −0.1%, and 3.9%, respectively.ConclusionThe MRI component of Unity operates within the guidelines and recommendations for scanner performance and stability. Our findings support the recently published guidance in establishing clinically acceptable tolerance levels for image quality. Highly reproducible qMRI measurements are feasible in Unity.

On the distribution of angles between increasingly many short lattice vectors

Following Södergren, we consider a collection of random variables on the space Xn of unimodular lattices in dimension n: normalizations of the angles between the N=N(n) shortest vectors in a random unimodular lattice, and the volumes of spheres with radii equal to the lengths of these vectors. We investigate the expected values of certain functions (whose support depends on a parameter K=K(n)) evaluated at these random variables in the regime where K and N are allowed to tend to infinity with n at the rate KN=o(n1/6). Our main result is that as n⟶∞, these random variables exhibit a joint Poissonian and Gaussian behavior.

Self-Powered Electrical Impulse Chemotherapy for Oral Squamous Cell Carcinoma.

Oral squamous cell carcinoma (OSCC) is a common oral cancer of the head and neck, which causes tremendous physical and mental pain to people. Traditional chemotherapy usually results in drug resistance and side effects, affecting the therapy process. In this study, a self-powered electrical impulse chemotherapy (EIC) method based on a portable triboelectric nanogenerator (TENG) was established for OSCC therapy. A common chemotherapeutic drug, doxorubicin (DOX), was used in the experiment. The TENG designed with zigzag structure had a small size of 6 cm × 6 cm, which could controllably generate the fixed output of 200 V, 400 V and 600 V. The electrical impulses generated by the TENG increased the cell endocytosis of DOX remarkably. Besides, a simply and ingeniously designed microneedle electrode increased the intensity of electric field (EF) between two adjacent microneedle tips compared with the most used planar interdigital electrode at the same height, which was more suitable for three-dimensional (3D) cells or tissues. Based on the TENG, microneedle electrode and DOX, the self-powered EIC system demonstrated a maximal apoptotic cell ratio of 22.47% and a minimum relative 3D multicellular tumor sphere (MCTS) volume of 160% with the drug dosage of 1 μg mL−1.

The impact of target positioning error and tumor size on radiobiological parameters in robotic stereotactic radiosurgery for metastatic brain tumors.

This study aimed to evaluate the effect of target positioning error (TPE) on radiobiological parameters, such as tumor control probability (TCP) and normal tissue complication probability (NTCP), in stereotactic radiosurgery (SRS) for metastatic brain tumors of different sizes using CyberKnife. The reference SRS plans were created using the circular cone of the CyberKnife for each spherical gross tumor volume (GTV) with diameters (φ) of 5, 7.5, 10, 15, and 20mm, contoured on computed tomography images of the head phantom. Subsequently, plans involving TPE were created by shifting the beam center by 0.1-2.0mm in three dimensions relative to the reference plans using the same beam arrangements. Conformity index (CI), generalized equivalent uniform dose (gEUD)-based TCP, and NTCP of estimated brain necrosis were evaluated for each plan. When the gEUD parameter "a" was set to - 10, the CI and TCP for the reference plan at the φ5-mm GTV were 0.90 and 80.8%, respectively. The corresponding values for plans involving TPE of 0.5-mm, 1.0-mm, and 2.0-mm were 0.62 and 77.4%, 0.40 and 62.9%, and 0.12 and 7.2%, respectively. In contrast, the NTCP for all GTVs were the same. The TCP for the plans involving a TPE of 2-mm was 7.2% and 68.8% at the φ5-mm and φ20-mm GTV, respectively. The TPEs corresponding to a TCP reduction rate of 3% at the φ5-mm and φ20-mm GTV were 0.41 and 0.99mm, respectively. TPE had a significant effect on TCP in SRS for metastatic brain tumors using CyberKnife, particularly for small GTVs.

Reproducibility of Standardized Uptake Values Including Volume Metrics Between TOF-PET-MR and TOF-PET-CT.

PurposeTo investigate the reproducibility of tracer uptake measurements, including volume metrics, such as metabolic tumor volume (MTV) and tumor lesion glycolysis (TLG) obtained by TOF-PET-CT and TOF-PET-MR.Materials and MethodsEighty consecutive patients with different oncologic diagnoses underwent TOF-PET-CT (Discovery 690; GE Healthcare) and TOF-PET-MR (SIGNA PET-MR; GE Healthcare) on the same day with single dose−18F-FDG injection. The scan order, PET-CT following or followed by PET-MR, was randomly assigned. A spherical volume of interest (VOI) of 30 mm was placed on the liver in accordance with the PERCIST criteria. For liver, the maximum and mean standard uptake value for body weight (SUV) and lean body mass (SUL) were obtained. For tumor delineation, VOI with a threshold of 40 and 50% of SUVmax was used (VOI40 and VOI50). The SUVmax, SUVmean, SUVpeak, MTV and TLG were calculated. The measurements were compared between the two scanners.ResultsIn total, 80 tumor lesions from 35 patients were evaluated. There was no statistical difference observed in liver regions, whereas in tumor lesions, SUVmax, SUV mean, and SUVpeak of PET-MR were significantly underestimated (p < 0.001) in both VOI40 and VOI50. Among volume metrics, there was no statistical difference observed except TLG on VOI50 (p = 0.03). Correlation between PET-CT and PET-MR of each metrics were calculated. There was a moderate correlation of the liver SUV and SUL metrics (r = 0.63–0.78). In tumor lesions, SUVmax and SUVmean had a stronger correlation with underestimation in PET-MR on VOI 40 (SUVmax and SUVmean; r = 0.92 and 0.91 with slope = 0.71 and 0.72, respectively). In the evaluation of MTV and TLG, the stronger correlations were observed both on VOI40 (MTV and TLG; r = 0.75 and 0.92) and VOI50 (MTV and TLG; r = 0.88 and 0.95) between PET-CT and PET-MR.ConclusionPET metrics on TOF-PET-MR showed a good correlation with that of TOF-PET-CT. SUVmax and SUVpeak of tumor lesions were underestimated by 16% on PET-MRI. MTV with % threshold can be regarded as identical volumetric markers for both TOF-PET-CT and TOF-PET-MR.

Modeling and simulation of needle electrical impedance myography in nonhomogeneous isotropic skeletal muscle.

Needle electrical impedance myography (EIM) is a recently developed technique for neuromuscular evaluation. Despite its preliminary successful clinical application, further understanding is needed to aid interpreting EIM outcomes in nonhomogeneous skeletal muscle measurements. The framework presented models needle EIM measurements in a bidomain isotropic model. Finite element method (FEM) simulations verify the validity of our model predictions studying two cases: a spherical volume surrounded by tissue and a two-layered tissue. Our models show that EIM is influenced by the vicinity of tissue with different electrical properties. The apparent resistance, reactance and phase relative errors between our theoretical predictions and FEM simulations in the spherical volume case study are ≤0.2%, ≤1.2% and ≤1.0%, respectively. For the two-layered tissue model case study, the relative errors are ≤2%. We propose a bio-physics driven analytical framework describing needle EIM measurements in a nonhomogeneous bidomain tissue model. Our theoretical predictions may lead to new ways for interpreting needle EIM data in neuromuscular diseases that cause compositional changes in muscle content, e.g. connective tissue deposition within the muscle. These changes will manifest themselves by changing the electric properties of the conductor media and will impact impedance values.

Hot Extended Galaxy Halos around Local L* Galaxies from Sunyaev–Zeldovich Measurements

Abstract Most of the baryons in L* galaxies are unaccounted for and are predicted to lie in hot gaseous halos (T ∼ 106.5 K) that may extend beyond R 200. A hot gaseous halo will produce a thermal Sunyaev–Zeldovich signal that is proportional to the product of the gas mass and the mass-weighted temperature. To best detect this signal, we used a Needlet Independent Linear Combination all-sky Planck map that we produced from the most recent Planck data release, also incorporating WMAP data. The sample is 12 L* spiral galaxies with distances of 3−10 Mpc, which are spatially resolved so that contamination from the optical galaxy can be excluded. One galaxy, NGC 891, has a particularly strong SZ signal, and when excluding it, the stack of 11 galaxies is detected at about 4σ (declining with radius) and is extended to at least 250 kpc (≈R 200) at &gt;99% confidence. The gas mass within a spherical volume to a radius of 250 kpc is 9.8 ± 2.8 × 1010 M ⊙, for T avg = 3 × 106 K. This is about 30% of the predicted baryon content of the average galaxy (3.1 × 1011 M ⊙), and about equal to the mass of stars, disk gas, and warm halo gas. The remaining missing baryons (≈1.4 × 1011 M ⊙, 40%–50% of the total baryon content) are likely to be hot and extend to the 400–500 kpc volume, if not beyond. The result is higher than predictions, but within the uncertainties.