Measuring Image Resolution in Ultrasound Localization Microscopy

Abstract

The resolution of an imaging system is usually determined by the width of its point spread function and is measured using the Rayleigh criterion. For most system, it is in the order of the imaging wavelength. However, super resolution techniques such as localization microscopy in optical and ultrasound imaging can resolve features an order of magnitude finer than the wavelength. The classical description of spatial resolution no longer applies and new methods need to be developed.In optical localization microscopy, the Fourier Ring Correlation has showed to be an effective and practical way to estimate spatial resolution for Single Molecule Localization Microscopy data. In this work, we wish to investigate how this tool can provide a direct and universal estimation of spatial resolution in Ultrasound Localization Microscopy. Moreover, we discuss the concept of spatial sampling in Ultrasound Localization Microscopy and demonstrate how the Nyquist criterion for sampling drives the spatial/temporal resolution tradeoff.We measured spatial resolution on five different datasets over rodent's brain, kidney and tumor finding values between 11 m and 34 m for precision of localization between 11 m and 15 m. Eventually, we discuss from those in vivo datasets how spatial resolution in Ultrasound Localization Microscopy depends on both the localization precision and the total number of detected microbubbles.This study aims to offer a practical and theoretical framework for image resolution in Ultrasound Localization Microscopy.

3D Transcranial Ultrasound Localization Microscopy in the Rat Brain With a Multiplexed Matrix Probe

“…By exploiting the correlation of spatial frequency, it provided an overall measure, not based on a selected feature of the volume. For the current volume, the 2-sigma threshold [52], [54], [55] gave a resolution of 38 µm, slightly higher than the segmented vessels. This value could be improved by extending the acquisition time.…”

“…To further validate the resolution of our approach, the Fourier Shell Correlation (FSC) [52], [53] was computed. It provides a non-local estimation of the resolution by calculating the correlation of spatial frequencies.…”

“…The list of microbubble trajectories was split into two sub-population (odd and even indices) used to reconstruct two observations of the same volume. The 2-sigma threshold [52], [54], [55] was applied to get a spatial frequency resolution compared to an expected theoretical pure-noise. The 2-sigma curve is obtained with the number of voxels 𝑛(𝑅) in each correlation shell of spatial frequency 1/𝑅.…”

Microvascular Imaging with Super-Resolution Ultrasound

“…Next, the single microbubbles are isolated and localized [4]. The precision of this localization is a critical step in obtaining super-resolu-tion [5]. Instead of merely superposing each of the microbubble localizations, as done in super-resolution microscopy, the movements of the microbubbles as they follow the bloodstream between frames are used to create trajectories that can reveal microbubble velocity and direction [6][7][8][9][10].…”

“…Anschließend werden die einzelnen Mikrobläschen isoliert und lokalisiert [4]. Die Präzision dieser Lokalisierung ist ein entscheidender Schritt zur Erzielung der Superresolution [5]. Anstatt wie bei der Superresolution-Mikroskopie jede einzelne Lokalisierung der Mikrobläschen zu überlagern, werden die Bewegungen der Mikrobläschen, während sie zwischen den Bildern dem Blutstrom folgen, verwendet, um Trajektorien zu erstellen, die die Geschwindigkeit und Richtung der Mikrobläschen aufzeigen können [6][7][8][9][10].…”