Thermodynamics of an Empty Box.

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

Ultrasound Imaging.

Ultrasound imaging plays an important role in oncological imaging for more than five decades now. It can be applied in all tissues that are not occluded by bone or gas-filled regions. The quality of ultrasound images benefitted strongly from improved electronics and increased computational power. To the morphological imaging, several functional imaging methods were added: Flow visualization became possible by Doppler techniques and as a recent addition the elastic properties of tissues can be imaged by elastographic methods with transient shear wave imaging. In the beginning of molecular imaging, ultrasound with its contrast based on mechanical tissue properties was an unlikely candidate to play a role. However, with contrast agents consisting of micrometer-sized gas bubbles, which can be imaged with high sensitivity, ligands addressing targets in the vascular wall could be used. Because even single bubbles can be detected, this led to various ultrasound molecular imaging techniques and the ongoing development of clinical molecular contrast media. In this chapter, the basic properties of ultrasonic imaging like its contrast mechanisms and spatiotemporal resolution are discussed. The image formation and its ongoing change from line-oriented scanning to full-volume reconstructions are explained. Then, the ultrasound contrast media and imaging techniques are introduced and emerging new methods like super-resolution vascular imaging demonstrate the ongoing development in this field.

[Perforation as a delayed complication after endoscopic full-thickness resection in a recurrent adenoma of the sigmoid]. / Perforation als Spätkomplikation nach endoskopischer Vollwandresektion eines Rezidivadenoms im Colon sigmoideum.

The endoscopic full-thickness resection (EFTR) is established in ablation of recurrent colorectal adenomas, which cannot be removed by endoscopic resection in cases of fibrosis. The EFTR can be applied with low risk, in one step, with the use of special devices, such as the full-thickness resection device (FTRD®). The main risks described in literature are bleeding and perforations. The mentioned perforations were explained by previous defects of the device system or patient-related predisposed parameters for perforation.We report the case of a 55-year old woman who underwent an endoscopic full-thickness resection with the FTRD® due to a recurrent adenoma with high-grade intraepithelial neoplasm in the sigmoid. After primary uncomplicated development, she presented with a secondary perforation with purulent peritonitis seven days after intervention, so a sigmoid-resection was necessary. There were no signs of defects with the FTRD® system or patient-related predisposed parameters, which prefer a perforation.Our case-report demonstrates the necessity for clinical follow up, after primary uncomplicated endoscopic full-thickness resection, to recognize delayed complications.

Unilateral deep brain stimulation suppresses alpha and beta oscillations in sensorimotor cortices.

Deep brain stimulation (DBS) is an established therapy to treat motor symptoms in movement disorders such as Parkinson's disease (PD). The mechanisms leading to the high therapeutic effectiveness of DBS are poorly understood so far, but modulation of oscillatory activity is likely to play an important role. Thus, investigating the effect of DBS on cortical oscillatory activity can help clarifying the neurophysiological mechanisms of DBS. Here, we aimed at scrutinizing changes of cortical oscillatory activity by DBS at different frequencies using magnetoencephalography (MEG). MEG data from 17 PD patients were acquired during DBS of the subthalamic nucleus (STN) the day after electrode implantation and before implanting the pulse generator. We stimulated the STN unilaterally at two different stimulation frequencies, 130 Hz and 340 Hz using an external stimulator. Data from six patients had to be discarded due to strong artefacts and two other datasets were excluded since these patients were not able to finalize the paradigm. After DBS artefact removal, power spectral density (PSD) values of MEG were calculated for each individual patient and averaged over the group. DBS at both 130 Hz and 340 Hz led to a widespread suppression of cortical alpha/beta band activity (8-22 Hz) specifically over bilateral sensorimotor cortices. No significant differences were observed between the two stimulation frequencies. Our finding of a widespread suppression of cortical alpha/beta band activity is particularly interesting as PD is associated with pathologically increased levels of beta band activity in the basal ganglia-thalamo-cortical circuit. Therefore, suppression of such oscillatory activity might be an essential effect of DBS for relieving motor symptoms in PD and can be achieved at different stimulation frequencies above 100 Hz.

Entropy and Geometric Objects.

Different notions of entropy can be identified in different scientific communities: (i) the thermodynamic sense; (ii) the information sense; (iii) the statistical sense; (iv) the disorder sense; and (v) the homogeneity sense. Especially the "disorder sense" and the "homogeneity sense" relate to and require the notion of space and time. One of the few prominent examples relating entropy to both geometry and space is the Bekenstein-Hawking entropy of a Black Hole. Although this was developed for describing a physical object-a black hole-having a mass, a momentum, a temperature, an electrical charge, etc., absolutely no information about this object's attributes can ultimately be found in the final formulation. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes such as an area A-the area of the event horizon of the black hole, a length LP-the Planck length, and a factor 1/4. A purely geometric approach to this formulation will be presented here. The approach is based on a continuous 3D extension of the Heaviside function which draws on the phase-field concept of diffuse interfaces. Entropy enters into the local and statistical description of contrast or gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formulation is ultimately derived for a geometric sphere based solely on geometric-statistical considerations.

Towards a metadata scheme for the description of materials - the description of microstructures.

The property of any material is essentially determined by its microstructure. Numerical models are increasingly the focus of modern engineering as helpful tools for tailoring and optimization of custom-designed microstructures by suitable processing and alloy design. A huge variety of software tools is available to predict various microstructural aspects for different materials. In the general frame of an integrated computational materials engineering (ICME) approach, these microstructure models provide the link between models operating at the atomistic or electronic scales, and models operating on the macroscopic scale of the component and its processing. In view of an improved interoperability of all these different tools it is highly desirable to establish a standardized nomenclature and methodology for the exchange of microstructure data. The scope of this article is to provide a comprehensive system of metadata descriptors for the description of a 3D microstructure. The presented descriptors are limited to a mere geometric description of a static microstructure and have to be complemented by further descriptors, e.g. for properties, numerical representations, kinetic data, and others in the future. Further attributes to each descriptor, e.g. on data origin, data uncertainty, and data validity range are being defined in ongoing work. The proposed descriptors are intended to be independent of any specific numerical representation. The descriptors defined in this article may serve as a first basis for standardization and will simplify the data exchange between different numerical models, as well as promote the integration of experimental data into numerical models of microstructures. An HDF5 template data file for a simple, three phase Al-Cu microstructure being based on the defined descriptors complements this article.

Optimized SNR simultaneous multispectral photoacoustic imaging with laser diodes.

Multispectral photoacoustic laser diode systems have multiple wavelengths available simultaneously. In addition to multispectral imaging, this can be exploited to increase the signal to noise ratio (SNR) by combining these wavelengths to form a combined image, but at the loss of spectral information. Here, a novel signal processing concept is introduced, which optimizes the SNR in the reconstructions of single wavelength data from combined acquisitions while simultaneously permitting to obtain a higher SNR fused image from the same data. The concept is derived for an arbitrary number of wavelengths; it is also applicable at low pulse repetition frequencies. The concept is applied in an experiment using two wavelengths, verifying the theoretical results.

Gradient Spin Echo (GraSE) imaging for fast myocardial T2 mapping.

BACKGROUND: Quantitative Cardiovascular Magnetic Resonance (CMR) techniques have gained high interest in CMR research. Myocardial T2 mapping is thought to be helpful in diagnosis of acute myocardial conditions associated with myocardial edema. In this study we aimed to establish a technique for myocardial T2 mapping based on gradient-spin-echo (GraSE) imaging. METHODS: The local ethics committee approved this prospective study. Written informed consent was obtained from all subjects prior to CMR. A modified GraSE sequence allowing for myocardial T2 mapping in a single breath-hold per slice using ECG-triggered acquisition of a black blood multi-echo series was developed at 1.5 Tesla. Myocardial T2 relaxation time (T2-RT) was determined by maximum likelihood estimation from magnitude phased-array multi-echo data. Four GraSE sequence variants with varying number of acquired echoes and resolution were evaluated in-vitro and in 20 healthy volunteers. Inter-study reproducibility was assessed in a subset of five volunteers. The sequence with the best overall performance was further evaluated by assessment of intra- and inter-observer agreement in all volunteers, and then implemented into the clinical CMR protocol of five patients with acute myocardial injury (myocarditis, takotsubo cardiomyopathy and myocardial infarction). RESULTS: In-vitro studies revealed the need for well defined sequence settings to obtain accurate T2-RT measurements with GraSE. An optimized 6-echo GraSE sequence yielded an excellent agreement with the gold standard Carr-Purcell-Meiboom-Gill sequence. Global myocardial T2 relaxation times in healthy volunteers was 52.2 ± 2.0 ms (mean ± standard deviation). Mean difference between repeated examinations (n = 5) was -0.02 ms with 95% limits of agreement (LoA) of [-4.7; 4.7] ms. Intra-reader and inter-reader agreement was excellent with mean differences of -0.1 ms, 95% LoA = [-1.3; 1.2] ms and 0.1 ms, 95% LoA = [-1.5; 1.6] ms, respectively (n = 20). In patients with acute myocardial injury global myocardial T2-RTs were prolonged (mean: 61.3 ± 6.7 ms). CONCLUSION: Using an optimized GraSE sequence CMR allows for robust, reliable, fast myocardial T2 mapping and quantitative tissue characterization. Clinically, the GraSE-based T2-mapping has the potential to complement qualitative CMR in patients with acute myocardial injuries.

Low-Energy Ultrasound Treatment Improves Regional Tumor Vessel Infarction by Retargeted Tissue Factor.

OBJECTIVES: To enhance the regional antitumor activity of the vascular-targeting agent truncated tissue factor (tTF)-NGR by combining the therapy with low-energy ultrasound (US) treatment. METHODS: For the in vitro US exposure of human umbilical vein endothelial cells (HUVECs), cells were put in the focus of a US transducer. For analysis of the US-induced phosphatidylserine (PS) surface concentration on HUVECs, flow cytometry was used. To demonstrate the differences in the procoagulatory efficacy of TF-derivative tTF-NGR on binding to HUVECs with a low versus high surface concentration of PS, we performed factor X activation assays. For low-energy US pretreatment, HT1080 fibrosarcoma xenotransplant-bearing nude mice were treated by tumor-regional US-mediated stimulation (ie, destruction) of microbubbles. The therapy cohorts received the tumor vessel-infarcting tTF-NGR protein with or without US pretreatment (5 minutes after US stimulation via intraperitoneal injection on 3 consecutive days). RESULTS: Combination therapy experiments with xenotransplant-bearing nude mice significantly increased the antitumor activity of tTF-NGR by regional low-energy US destruction of vascular microbubbles in tumor vessels shortly before application of tTF-NGR (P < .05). Mechanistic studies proved the upregulation of anionic PS on the outer leaflet of the lipid bilayer of endothelial cell membranes by low-energy US and a consecutive higher potential of these preapoptotic endothelial cells to activate coagulation via tTF-NGR and coagulation factor X as being a basis for this synergistic activity. CONCLUSIONS: Combining retargeted tTF to tumor vessels with proapoptotic stimuli for the tumor vascular endothelium increases the antitumor effects of tumor vascular infarction. Ultrasound treatment may thus be useful in this respect for regional tumor therapy.

Ultrafast volumetric B1 (+) mapping for improved radiofrequency shimming in 3 tesla body MRI.

PURPOSE: To evaluate the use of the recently proposed ultrafast B1 (+) mapping approach DREAM (Dual Refocusing Echo Acquisition Mode) for a refinement of patient adaptive radiofrequency (RF) shimming. MATERIALS AND METHODS: Volumetric DREAM B1 (+) calibration scans centered in the upper abdomen were acquired in 20 patients and three volunteers with written informed consent at a clinical dual source 3 Tesla (T) MR system. Based on these data, RF transmit settings were optimized by central-slice based RF-shimming (CS-RF shim) and by a refined, multi-slice adaptive approach (MS-RF shim). Simulations were performed to compare flip angle accuracy and B1 (+) homogeneity (cv = stddev/mean) achieved by CS-RF shim versus MS-RF shim for transversal and coronal slices, and for volume shimming on the spine. RESULTS: By MS-RF shim, mean deviation from nominal flip angle was reduced to less than 11% in all slices, all targets, and all subjects. Relative improvements in B1 (+) cv (MS-RF shim versus CS-RF) were up to 14%/39%/47% in transversal slices/coronal slices/ spine area. CONCLUSION: Volumetric information about B1 (+) can be used to further improve the accuracy and homogeneity of the B1 (+) field yielding higher diagnostic confidence, and will also be of value for various quantitative methods which are sensitive to flip angle imperfections.

Comment on "So you think you can DAS? A viewpoint on delay-and-sum beamforming" [Ultrasonics 111 (2021) 106309].

It is shown herein that Perrot et al., who reviewed delay-and-sum beamforming for ultrafast ultrasound imaging in [Ultrasonics 111 (2021) 106309], misinterpreted the purpose of dynamic receive apertures. Such apertures widen with the focal length as a function of a given f-number and improve the image quality by suppressing grating lobes. Perrot et al., however, attributed erroneously the image quality improvement to suppression of measurement noise and, in doing so, proposed a suboptimal method to determine an f-number.

ULTRA-SR Challenge: Assessment of Ultrasound Localization and TRacking Algorithms for Super-Resolution Imaging.

With the widespread interest and uptake of super-resolution ultrasound (SRUS) through localization and tracking of microbubbles, also known as ultrasound localization microscopy (ULM), many localization and tracking algorithms have been developed. ULM can image many centimeters into tissue in-vivo and track microvascular flow non-invasively with sub-diffraction resolution. In a significant community effort, we organized a challenge, Ultrasound Localization and TRacking Algorithms for Super-Resolution (ULTRA-SR). The aims of this paper are threefold: to describe the challenge organization, data generation, and winning algorithms; to present the metrics and methods for evaluating challenge entrants; and to report results and findings of the evaluation. Realistic ultrasound datasets containing microvascular flow for different clinical ultrasound frequencies were simulated, using vascular flow physics, acoustic field simulation and nonlinear bubble dynamics simulation. Based on these datasets, 38 submissions from 24 research groups were evaluated against ground truth using an evaluation framework with six metrics, three for localization and three for tracking. In-vivo mouse brain and human lymph node data were also provided, and performance assessed by an expert panel. Winning algorithms are described and discussed. The publicly available data with ground truth and the defined metrics for both localization and tracking present a valuable resource for researchers to benchmark algorithms and software, identify optimized methods/software for their data, and provide insight into the current limits of the field. In conclusion, Ultra-SR challenge has provided benchmarking data and tools as well as direct comparison and insights for a number of the state-of-the art localization and tracking algorithms.

Ultrasound localization microscopy.

Ultrasound Localization Microscopy (ULM) is an emerging technique that provides impressive super-resolved images of microvasculature, i.e., images with much better resolution than the conventional diffraction-limited ultrasound techniques and is already taking its first steps from preclinical to clinical applications. In comparison to the established perfusion or flow measurement methods, namely contrast-enhanced ultrasound (CEUS) and Doppler techniques, ULM allows imaging and flow measurements even down to the capillary level. As ULM can be realized as a post-processing method, conventional ultrasound systems can be used for. ULM relies on the localization of single microbubbles (MB) of commercial, clinically approved contrast agents. In general, these very small and strong scatterers with typical radii of 1-3 µm are imaged much larger in ultrasound images than they actually are due to the point spread function of the imaging system. However, by applying appropriate methods, these MBs can be localized with sub-pixel precision. Then, by tracking MBs over successive frames of image sequences, not only the morphology of vascular trees but also functional information such as flow velocities or directions can be obtained and visualized. In addition, quantitative parameters can be derived to describe pathological and physiological changes in the microvasculature. In this review, the general concept of ULM and conditions for its applicability to microvessel imaging are explained. Based on this, various aspects of the different processing steps for a concrete implementation are discussed. The trade-off between complete reconstruction of the microvasculature and the necessary measurement time as well as the implementation in 3D are reviewed in more detail, as they are the focus of current research. Through an overview of potential or already realized preclinical and clinical applications - pathologic angiogenesis or degeneration of vessels, physiological angiogenesis, or the general understanding of organ or tissue function - the great potential of ULM is demonstrated.

Frequency-Dependent F-Number Suppresses Grating Lobes and Improves the Lateral Resolution in Coherent Plane-Wave Compounding.

Ultrafast imaging modes, such as coherent plane-wave compounding (CPWC), increase image uniformity and reduce grating lobe artifacts by dynamic receive apertures. The focal length and the desired aperture width maintain a given ratio, which is called the F -number. Fixed F -numbers, however, exclude useful low-frequency components from the focusing and reduce the lateral resolution. Herein, this reduction is avoided by a frequency-dependent F -number. This F -number derives from the far-field directivity pattern of a focused aperture and can be expressed in closed form. The F -number, at low frequencies, widens the aperture to improve the lateral resolution. The F -number, at high frequencies, narrows the aperture to avoid lobe overlaps and suppress grating lobes. Phantom and in vivo experiments with a Fourier-domain beamforming algorithm validated the proposed F -number in CPWC. The lateral resolution, which was measured by the median lateral full-widths at half-maximum of wires, improved by up to 46.8% and 14.9% in a wire and a tissue phantom, respectively, in comparison to fixed F -numbers. Grating lobe artifacts, which were measured by the median peak signal-to-noise ratios of wires, reduced by up to 9.9 dB in comparison to the full aperture. The proposed F -number thus outperformed F -numbers that were recently derived from the directivity of the array elements.

A Single-Shot Harmonic Imaging Approach Utilizing Deep Learning for Medical Ultrasound.

Tissue Harmonic Imaging (THI) is an invaluable tool in clinical ultrasound owing to its enhanced contrast resolution and reduced reverberation clutter in comparison to fundamental mode imaging. However, harmonic content separation based on high pass filtering suffers from potential contrast degradation or lower axial resolution due to spectral leakage. Whereas nonlinear multi-pulse harmonic imaging schemes, such as amplitude modulation and pulse inversion, suffer from a reduced framerate and comparatively higher motion artifacts due to the necessity of at least two pulse echo acquisitions. To address this problem, we propose a deep-learning-based single-shot harmonic imaging technique capable of generating comparable image quality to pulse amplitude modulation methods, yet at a higher framerate and with fewer motion artifacts. Specifically, an asymmetric convolutional encoder-decoder structure is designed to estimate the combination of the echoes resulting from the half-amplitude transmissions using the echo produced from the full amplitude transmission as input. The echoes were acquired with the checkerboard amplitude modulation technique for training. The model was evaluated across various targets and samples to illustrate generalizability as well as the possibility and impact of transfer learning. Furthermore, for possible interpretability of the network, we investigate if the latent space of the encoder holds information on the nonlinearity parameter of the medium. We demonstrate the ability of the proposed approach to generate harmonic images with a single firing that are comparable to those from a multi-pulse acquisition.

Size-dependent multispectral photoacoustic response of solid and hollow gold nanoparticles.

Photoacoustic (PA) imaging attracts a great deal of attention as an innovative modality for longitudinal, non-invasive, functional and molecular imaging in oncology. Gold nanoparticles (AuNPs) are identified as superior, NIR-absorbing PA contrast agents for biomedical applications. Until now, no systematic comparison of the optical extinction and PA efficiency of water-soluble AuNPs of various geometries and small sizes has been performed. Here spherical AuNPs with core diameters of 1.0, 1.4 and 11.2 nm, nanorods with longitudinal/transversal elongation of 38/9 and 44/12 nm and hollow nanospheres with outer/inner diameters of 33/19, 57/30, 68/45 and 85/56 nm were synthesized. The diode laser set-up with excitations at 650, 808, 850 and 905 nm allowed us to correlate the molar PA signal intensity with the molar extinction of the respective AuNPs. Deviations were explained by differences in heat transfer from the particle to the medium and, for larger particles, by the scattering of light. The molar PA intensity of 1.0 nm AuNPs was comparable to the commonly used organic dye methylene blue, and rapidly increased with the lateral size of AuNPs.

Identification of static nonlinearities by sinusoidal excitation with variable DC offsets.

When identifying nonlinear systems with input-output measurements, a suitable test signal must be selected. Nonlinear systems are almost always in a cascade with linear systems, i.e., a Wiener-Hammerstein type system cascade. A suitable test signal is preferably less influenced by the linear systems and is therefore sinusoidal, if time-varying signals are required for the measurement principle, e.g., for induction or vibration measurements. Then, a sinusoidal excitation with different DC offsets is a suitable signal to analyze a static nonlinear system in a Wiener-Hammerstein type cascade by measuring the cascade output at higher harmonics of the input frequency in a steady state, e.g., by using sensitive lock-in techniques. To calculate the cascade output given the input signal or to reconstruct the static nonlinear system also given the output signal, the transfer function of the DC offset at the nonlinear system input to the higher harmonics at the nonlinear system output is required. Those transfer functions are calculated here with emphasis on the first harmonic component. The reconstruction of a static nonlinear system is demonstrated in a simple simulation scenario by inverse filtering, i.e., deconvolution, with the derived transfer function. It is pointed out that a commonly made small signal assumption to the test signal is bypassed with the deconvolution method, which can lead to more precise measurements in applications due to a higher signal-to-noise ratio at the cascade output.

Effects of contrast-enhanced ultrasound treatment on neoadjuvant chemotherapy in breast cancer.

Purpose: Preclinical and clinical data indicate that contrast-enhanced ultrasound can enhance tumor perfusion and vessel permeability, thus, improving chemotherapy accumulation and therapeutic outcome. Therefore, we investigated the effects of high mechanical index (MI) contrast-enhanced Doppler ultrasound (CDUS) on tumor perfusion in breast cancer. Methods: In this prospective study, breast cancer patients were randomly assigned to receive either 18 minutes of high MI CDUS during chemotherapy infusion (n = 6) or chemotherapy alone (n = 5). Tumor perfusion was measured before and after at least six chemotherapy cycles using motion-model ultrasound localization microscopy. Additionally, acute effects of CDUS on vessel perfusion and chemotherapy distribution were evaluated in mice bearing triple-negative breast cancer (TNBC). Results: Morphological and functional vascular characteristics of breast cancer in patients were not significantly influenced by high MI CDUS. However, complete clinical tumor response after neoadjuvant chemotherapy was lower in high MI CDUS-treated (1/6) compared to untreated patients (4/5) and size reduction of high MI CDUS treated tumors tended to be delayed at early chemotherapy cycles. In mice with TNBC high MI CDUS decreased the perfused tumor vessel fraction (p < 0.01) without affecting carboplatin accumulation or distribution. Higher vascular immaturity and lower stromal stabilization may explain the stronger vascular response in murine than human tumors. Conclusion: High MI CDUS had no detectable effect on breast cancer vascularization in patients. In mice, the same high MI CDUS setting did not affect chemotherapy accumulation although strong effects on the tumor vasculature were detected histologically. Thus, sonopermeabilization in human breast cancers might not be effective using high MI CDUS protocols and future applications may rather focus on low MI approaches triggering microbubble oscillations instead of destruction. Furthermore, our results show that there are profound differences in the response of mouse and human tumor vasculature to high MI CDUS, which need to be further explored and considered in clinical translation.

Multispectral photoacoustic coded excitation imaging using unipolar orthogonal Golay codes.

We present a method to speed up the acquisition of multispectral photoacoustic data sets by using unipolar orthogonal Golay codes as excitation sequences for the irradiation system. Multispectral photoacoustic coded excitation (MS-PACE) allows acquiring photoacoustic data sets for two irradiation wavelengths simultaneously and separating them afterwards, thus improving the SNR or speeding up the measurement. We derive an analytical estimation of the SNR improvement using MS-PACE compared to time equivalent averaging. We demonstrate the feasibility of the method by successfully imaging a phantom composed of two dyes using unipolar orthogonal Golay codes as excitation sequence for two high power laser diodes operating at two different wavelengths. The experimental results show very good agreement with the theoretical predictions.

Assessing Vessel Reconstruction in Ultrasound Localization Microscopy by Maximum Likelihood Estimation of a Zero-Inflated Poisson Model.

In clinical applications of super-resolution ultrasound imaging, it is often not possible to achieve a full reconstruction of the microvasculature within a limited measurement time. This makes the comparison of studies and quantitative parameters of vascular morphology and perfusion difficult. Therefore, saturation models were proposed to predict adequate measurement times and estimate the degree of vessel reconstruction. Here, we derive a statistical model for the microbubble counts in super-resolution voxels by a zero-inflated Poisson (ZIP) process. In this model, voxels either belong to vessels with probability Pv and count events with Poisson rate Λ , or they are empty and remain zero. In this model, Pv represents the vessel voxel density in the super-resolution image after infinite measurement time. For the parameters Pv and Λ , we give Cramér-Rao lower bounds (CRLBs) for the estimation variance and derive maximum likelihood estimators (MLEs) in a novel closed-form solution. These can be calculated with knowledge of only the counts at the end of the acquisition time. The estimators are applied to preclinical and clinical data and the MLE outperforms alternative estimators proposed before. The estimated degree of reconstruction lies between 38% and 74% after less than 90 s. Vessel probability Pv ranged from 4% to 20%. The rate parameter Λ was estimated in the range of 0.5-1.3 microbubbles/voxel. For these parameter ranges, the CRLB gives standard deviations of less than 2%, which supports that the parameters can be estimated with good precision already for limited acquisition times.