Estimation of the probability density function of random displacements from images

Ahmadzadegan, Adib; Ardekani, Arezoo M.; Vlachos, Pavlos P.

doi:10.1103/physreve.102.033305

Cited by 10 publications

(11 citation statements)

References 31 publications

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“…The colocalization percentage was evaluated based on the value of the peak of the spatial cross-correlation of the two images. To account for different illumination techniques and normalize the intensity range in the images, the cross-correlation peak was normalized by the geometric average of the autocorrelation peak of each image. − The percentage of colocalization was obtained using the following equation % colocalization = 100 % × max ( I 1 ⊗ I 2 ) max ( I 1 ⊗ I 1 ) × I 2 ⊗ I 2 where I 1 and I 2 are the two images and ⊗ denotes a 2D spatial convolution.…”

Section: Methodsmentioning

confidence: 99%

Interpenetrating Networks of Collagen and Hyaluronic Acid That Serve as In Vitro Tissue Models for Assessing Macromolecular Transport

Torres,

Meng,

Bhattacharya

et al. 2023

Biomacromolecules

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High-fidelity preclinical in vitro tissue models can reduce the failure rate of drugs entering clinical trials. Collagen and hyaluronic acid (HA) are major components of the extracellular matrix of many native tissues and affect therapeutic macromolecule diffusion and recovery through tissues. Although collagen and HA are commonly used in tissue engineering, the physical and mechanical properties of these materials are variable and depend highly on processing conditions. In this study, HA was chemically modified and crosslinked via hydrazone bonds to form interpenetrating networks of crosslinked HA (HAX) with collagen (Col). These networks enabled a wide range of mechanical properties, including stiffness and swellability, and microstructures, such as pore morphology and size, that can better recapitulate diverse tissues. We utilized these interpenetrating ColHAX hydrogels as in vitro tissue models to examine macromolecular transport and recovery for early-stage drug screening. Hydrogel formulations with varying collagen and HAX concentrations imparted different gel properties based on the ratio of collagen to HAX. These gels were stable and swelled up to 170% of their original mass, and the storage moduli of the ColHAX gels increased over an order of magnitude by increasing collagen and HA concentration. Interestingly, when HAX concentration was constant and collagen concentration increased, both the pore size and spatial colocalization of collagen and HA increased. HA in the system dominated the ζ-potentials of the gels. The hydrogel and macromolecule properties impacted the mass transport and recovery of lysozyme, β-lactoglobulin, and bovine serum albumin (BSA) from the ColHAX gels�large molecules were largely impacted by mesh size, whereas small molecules were influenced primarily by electrostatic forces. Overall, the tunable properties demonstrated by the ColHAX hydrogels can be used to mimic different tissues for early-stage assays to understand drug transport and its relationship to matrix properties.

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Section: Methodsmentioning

confidence: 99%

Interpenetrating Networks of Collagen and Hyaluronic Acid That Serve as In Vitro Tissue Models for Assessing Macromolecular Transport

Torres,

Meng,

Bhattacharya

et al. 2023

Biomacromolecules

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“…The confocal image series were then processed using an image-based probability estimation of displacement (iPED) method to find the average diffusion coefficient of the droplets in the solution [30]. The Stokes-Einstein equation was used to determine the size of the particles based on the measured diffusion coefficient, solution viscosity, and temperature [31].…”

Section: Nanodroplet Characterizationmentioning

confidence: 99%

Stable Thermally-Modulated Nanodroplet Ultrasound Contrast Agents

et al. 2021

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Liquid perfluorocarbon-based nanodroplets are stable enough to be used in extravascular imaging, but provide limited contrast enhancement due to their small size, incompressible core, and small acoustic impedance mismatch with biological fluids. Here we show a novel approach to overcoming this limitation by using a heating–cooling cycle, which we will refer to as thermal modulation (TM), to induce echogenicity of otherwise stable but poorly echogenic nanodroplets without triggering a transient phase shift. We apply thermal modulation to high-boiling point tetradecafluorohexane (TDFH) nanodroplets stabilized with a bovine serum albumin (BSA) shell. BSA-TDFH nanodroplets with an average diameter under 300 nanometers showed an 11.9 ± 5.4 mean fold increase in echogenicity on the B-mode and a 13.9 ± 6.9 increase on the nonlinear contrast (NLC) mode after thermal modulation. Once activated, the particles maintained their enhanced echogenicity (p < 0.001) for at least 13 h while retaining their nanoscale size. Our data indicate that thermally modulated nanodroplets can potentially serve as theranostic agents or sensors for various applications of contrast-enhanced ultrasound.

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“…To address this gap, we developed a method termed the moment of probability of displacement (MPD). We based our approach on directly estimating the Probability Density Function (PDF) of particles' displacement using the image-based probability estimation of displacement (iPED) [45,46]. This method finds the PDF by deconvolving the ensemble autocorrelation from the ensemble cross-correlation.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty estimation for ensemble particle image velocimetry

Ahmadzadegan

Bhattacharya

Ardekani

et al. 2022

Meas. Sci. Technol.

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We present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (PIV) measurements. The ensemble PIV technique is widely used when the cross-correlation signal-to-noise ratio is insufficient to perform a reliable instantaneous velocity measurement. Despite the utility of ensemble PIV, uncertainty quantification for this type of measurement has not been studied. Here we propose a method for finding the uncertainty directly from the probability density function of displacements found by deconvolving the ensemble cross-correlation from the ensemble autocorrelation. We then find the second moment of the probability density function and apply a scaling factor to report uncertainty in velocity measurement. We term this method as the Moment of Probability of Displacement (MPD). We assess MPD's performance with synthetic and experimental images. We show that predicted uncertainties agree well with the expected root mean square of the error in the velocity measurements over a wide range of image and flow conditions. MPD shows good sensitivity to various PIV error sources with around 86% accuracy in matching the root mean square of error in the baseline data sets. So, MPD establishes itself as a reliable uncertainty quantification algorithm for ensemble PIV. We compared the results of MPD against one of the existing instantaneous PIV uncertainty approaches, Moment of Correlation. We adapted the Moment of Correlation approach for ensemble PIV however its primary limitations remain the assumption of Gaussian probability density function of displacements and Gaussian particles' intensity profile. In addition, our analysis shows that ensemble Moment of Correlation consistently underestimates the uncertainty, while MPD outperforms that and removes the limiting Gaussian assumption for the particle and probability density function, thus overcomes the limitations of the Moment of Correlation.

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Estimation of the probability density function of random displacements from images

Cited by 10 publications

References 31 publications

Interpenetrating Networks of Collagen and Hyaluronic Acid That Serve as In Vitro Tissue Models for Assessing Macromolecular Transport

Interpenetrating Networks of Collagen and Hyaluronic Acid That Serve as In Vitro Tissue Models for Assessing Macromolecular Transport

Stable Thermally-Modulated Nanodroplet Ultrasound Contrast Agents

Uncertainty estimation for ensemble particle image velocimetry

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