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1.
Article in English | MEDLINE | ID: mdl-38915290

ABSTRACT

BACKGROUND: The stomach's ability to store, mix, propel, and empty its content requires highly coordinated motor functions. However, current diagnostic tools cannot simultaneously assess these motor processes. This study aimed to use magnetic resonance imaging (MRI) to map multifaceted gastric motor functions, including accommodation, tonic and peristaltic contractions, and emptying, through a single non-invasive experiment for both humans and rats. METHODS: Ten humans and ten Sprague-Dawley rats consumed MRI-visible semi-solid meals and underwent MRI scans. We used a surface model to analyze MRI data, capturing the deformation of the stomach wall upon ingestion or during digestion. We inferred muscle activity, mapped motor processes, parcellated the stomach into functional regions, and revealed cross-species distinctions. RESULTS: In humans, both the fundus and antrum distended post-meal, followed by sustained tonic contractions to regulate intragastric pressure. Peristaltic contractions initiate from the distal fundus, including three concurrent wavefronts oscillating at 3.3 cycles per minute (cpm) and traveling at 1.7 to 2.9 mm/s. These motor functions facilitate linear gastric emptying with a 61-min half-time. In contrast, rats exhibited peristalsis from the mid-corpus, showing two wavefronts oscillating at 5 cpm and traveling at 0.3 to 0.9 mm/s. For both species, motility features allowed functional parcellation of the stomach along a mid-corpus division. CONCLUSIONS: This study maps region- and species-specific gastric motor functions. We demonstrate the value of MRI with surface modeling in understanding gastric physiology and its potential to become a new standard for clinical and preclinical investigations of gastric disorders at both individual and group levels.

2.
Magn Reson Med ; 2024 Apr 23.
Article in English | MEDLINE | ID: mdl-38651172

ABSTRACT

PURPOSE: To observe the growth and resolution of decompression gas bubbles in the spinal cord of live rats in real time using MRI. METHODS: We constructed an MRI-compatible pressure chamber system to visualize gas bubble dynamics in deep tissues in real time. The system pressurizes and depressurizes rodents inside an MRI scanner and monitors their respiratory rate, heart rate, and body temperature while providing gaseous anesthesia under pressure during the experiments. RESULTS: We observed the formation of decompression gas bubbles in the spinal cord of rats after compression to 7.1 bar absolute and rapid decompression inside the MRI scanner while maintaining continuous gaseous anesthesia and vital monitoring. CONCLUSION: We have shown the direct observation of decompression gas bubble formation in real time by MRI in live, anesthetized rats.

3.
IEEE Trans Biomed Eng ; 70(7): 2046-2057, 2023 07.
Article in English | MEDLINE | ID: mdl-37018592

ABSTRACT

OBJECTIVE: Gastrointestinal magnetic resonance imaging (MRI) provides rich spatiotemporal data about the movement of the food inside the stomach, but does not directly report muscular activity on the stomach wall. Here we describe a novel approach to characterize the motility of the stomach wall that drives the volumetric changes of the ingesta. METHODS: A neural ordinary differential equation was optimized to model a diffeomorphic flow that ascribed the deformation of the stomach wall to a continuous biomechanical process. Driven by this diffeomorphic flow, the surface of the stomach progressively changes its shape over time, while preserving its topology and manifoldness. RESULTS: We tested this approach with MRI data collected from 10 rats under a lightly anesthetized condition, and demonstrated accurate characterization of gastric motor events with an error in the order of sub-millimeters. Uniquely, we characterized gastric anatomy and motility with a surface coordinate system common at both individual and group levels. Functional maps were generated to reveal the spatial, temporal, and spectral characteristics of muscle activity and its coordination across different regions. The peristalsis at the distal antrum had a dominant frequency and peak-to-peak amplitude of [Formula: see text] cycles per minute and [Formula: see text] mm, respectively. The relationship between muscle thickness and gastric motility was found to be distinct between two functional regions in the proximal and distal stomach. CONCLUSION: These results demonstrate the efficacy of using MRI to model gastric anatomy and function. SIGNIFICANCE: The proposed approach is expected to enable non-invasive and accurate mapping of gastric motility for preclinical and clinical studies.


Subject(s)
Gastric Emptying , Gastrointestinal Motility , Rats , Animals , Gastric Emptying/physiology , Gastrointestinal Motility/physiology , Stomach/diagnostic imaging , Stomach/physiology , Magnetic Resonance Imaging/methods , Muscles
4.
Philos Trans A Math Phys Eng Sci ; 380(2234): 20210324, 2022 Oct 17.
Article in English | MEDLINE | ID: mdl-36031828

ABSTRACT

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

5.
Article in English | MEDLINE | ID: mdl-32746229

ABSTRACT

An inexpensive, accurate focused ultrasound stereotactic targeting method guided by pretreatment magnetic resonance imaging (MRI) images for murine brain models is presented. An uncertainty of each sub-component of the stereotactic system was analyzed. The entire system was calibrated using clot phantoms. The targeting accuracy of the system was demonstrated with an in vivo mouse glioblastoma (GBM) model. The accuracy was quantified by the absolute distance difference between the prescribed and ablated points visible on the pre treatment and posttreatment MR images, respectively. A precalibration phantom study ( N = 6 ) resulted in an error of 0.32 ± 0.31, 0.72 ± 0.16, and 1.06 ± 0.38 mm in axial, lateral, and elevational axes, respectively. A postcalibration phantom study ( N = 8 ) demonstrated a residual error of 0.09 ± 0.01, 0.15 ± 0.09, and 0.47 ± 0.18 mm in axial, lateral, and elevational axes, respectively. The calibrated system showed significantly reduced ( ) error of 0.20 ± 0.21, 0.34 ± 0.24, and 0.28 ± 0.21 mm in axial, lateral, and elevational axes, respectively, in the in vivo GBM tumor-bearing mice ( N = 10 ).


Subject(s)
Imaging, Three-Dimensional , Magnetic Resonance Imaging , Animals , Brain/diagnostic imaging , Mice , Phantoms, Imaging , Stereotaxic Techniques
6.
Ann Biomed Eng ; 48(1): 329-341, 2020 Jan.
Article in English | MEDLINE | ID: mdl-31456089

ABSTRACT

Although widely used as a preclinical model for studying cardiovascular diseases, there is a scarcity of in vivo hemodynamic measurements of the naïve murine system in multiple arterial and venous locations, from head-to-toe, and across sex and age. The purpose of this study is to quantify cardiovascular hemodynamics in mice at different locations along the vascular tree while evaluating the effects of sex and age. Male and female, adult and aged mice were anesthetized and underwent magnetic resonance imaging. Data were acquired from four co-localized vessel pairs (carotid/jugular, suprarenal and infrarenal aorta/inferior vena cava (IVC), femoral artery/vein) at normothermia (core temperature 37 ± 0.2 °C). Influences of age and sex on average velocity differ by location in arteries. Average arterial velocities, when plotted as a function of distance from the heart, decrease nearly linearly from the suprarenal aorta to the femoral artery (adult and aged males: - 0.33 ± 0.13, R2 = 0.87; - 0.43 ± 0.10, R2 = 0.95; adult and aged females: - 0.23 ± 0.07, R2 = 0.91; - 0.23 ± 0.02, R2 = 0.99). Average velocity of aged males and average volumetric flow of aged males and females tended to be larger compared to adult comparators. With cardiovascular disease as the leading cause of death and with the implications of cardiovascular hemodynamics as important biomarkers for health and disease, this work provides a foundation for sex and age comparisons in pathophysiology by collecting and analyzing hemodynamic data for the healthy murine arterial and venous system from head-to-toe, across sex and age.


Subject(s)
Aging/physiology , Arteries/diagnostic imaging , Arteries/physiology , Regional Blood Flow , Sex Characteristics , Veins/diagnostic imaging , Veins/physiology , Animals , Female , Magnetic Resonance Imaging , Male , Mice, Inbred C57BL
7.
J Magn Reson ; 310: 106620, 2020 01.
Article in English | MEDLINE | ID: mdl-31743862

ABSTRACT

A novel displacement-encoding spin-echo-stimulated-echo MRI sequence (APGSTEi) was used to obtain full-volume 3D strain fields in samples of two soft materials, a silicone elastomer and an ovine ligament. The samples were stretched cyclically and imaged synchronously. The multi-slice imaging sequence employed a combination of hard and soft spin-echos with bipolar gradient pulses for spatial encoding and decoding, combined with rapid multi-slice spin echo readouts. The sequence minimized undesirable signal loss due to T2∗ and T2 decays, which occur in polymeric materials or in the presence of appreciable air-solid susceptibility contrast, a particular concern for irregularly shaped samples in high magnetic fields. The images' magnitudes were T1-weighted; their phase encoded displacements which occurred during a Δ = 400 ms storage interval separating encoding and decoding pulses. Unwanted residual signals were filtered using a Gaussian filter tailored to attain the desired noise floor. The experiments measured 3D deformation with a nominal resolution of 290 µm × 250 µm × 250 µm in a sample volume of 5.6 cm × 1.6 cm × 1.6 cm, in less than an hour.

8.
Int J Hyperthermia ; 36(1): 1137-1146, 2019.
Article in English | MEDLINE | ID: mdl-31744344

ABSTRACT

Background: Because of the importance of adrenoreceptors in regulating the cardiovascular (CV) system and the role of the CV system in thermoregulation, understanding the response to these two stressors is of interest. The purpose of this study was to assess changes of arterial geometry and function in vivo during thermal and ß-adrenergic stress induced in mice and quantified by MRI.Methods: Male mice were anesthetized and imaged at 7 T. Anatomical and functional data were acquired from the neck (carotid artery), torso (suprarenal and infrarenal aorta and iliac artery) and periphery (femoral artery). Intravenous dobutamine (tail vein catheter, 40 µg/kg/min, 0.12 mL/h) was used as ß-adrenergic stressor. Baseline and dobutamine data were acquired at minimally hypothermic (35 °C) and minimally hyperthermic (38 °C) core temperatures. Cross-sectional vessel area and maximum cyclic strain were measured across the cardiac cycle.Results: Vascular response varied by location and by core temperature. For minimally hypothermic conditions (35 °C), average, maximum and minimum areas decreased with dobutamine only at the suprarenal aorta (avg: -17.9%, max: -13.5%, min: -21.4%). For minimally hyperthermic conditions (38 °C), vessel areas decreased between baseline and dobutamine at the carotid (avg: -19.6%, max: -15.5%, min: -19.3%) and suprarenal aorta (avg: -24.2%, max: -17.4%, min: -17.3%); whereas, only the minimum vessel area decreased for the iliac artery (min: -14.4%). Maximum cyclic strain increased between baseline and dobutamine at the iliac artery for both conditions and at the suprarenal aorta at hyperthermic conditions.Conclusions: At hypothermic conditions, the vessel area response to dobutamine is diminished compared to hyperthermic conditions where the vessel area response mimics normothermic dobutamine conditions. The varied response emphasizes the need to monitor and control body temperature during medical conditions or treatments that may be accompanied by hypothermia, especially when vasoactive agents are used.


Subject(s)
Adrenergic beta-Agonists/therapeutic use , Fever/drug therapy , Hypothermia/drug therapy , Animals , Disease Models, Animal , Male , Mice
9.
J Magn Reson Imaging ; 49(1): 69-80, 2019 01.
Article in English | MEDLINE | ID: mdl-30291650

ABSTRACT

BACKGROUND: One of the primary biomechanical factors influencing arterial health is their deformation across the cardiac cycle, or cyclic strain, which is often associated with arterial stiffness. Deleterious changes in the cardiovascular system, e.g., increased arterial stiffness, can remain undetected until the system is challenged, such as under a cardiac stressor like dobutamine. PURPOSE: To quantify cyclic strain in mice at different locations along the arterial tree prior to and during dobutamine infusion, while evaluating the effects of sex and age. STUDY TYPE: Control/cohort study. ANIMAL MODEL: Twenty C57BL/6 mice; male, female; ∼12 and 24 weeks of age; n = 5 per group. FIELD STRENGTH/SEQUENCE: 7T; CINE MRI with 12 frames, velocity compensation, and prospective cardiac gating. ASSESSMENT: Prior to and during the infusion of dobutamine, Green-Lagrange circumferential cyclic strain was calculated from perimeter measurements derived from CINE data acquired at the carotid artery, suprarenal and infrarenal abdominal aorta, and iliac artery. STATISTICAL TESTS: Analysis of variance (ANOVA) followed by post-hoc tests was used to evaluate the influence of dobutamine, anatomical location, sex, and age. RESULTS: Heart rates did not differ between groups prior to or during dobutamine infusion (P = 0.87 and P = 0.08, respectively). Dobutamine increased cyclic strain in each group. Within a group, increases in strain were similar across arteries. At the suprarenal aorta, strain was reduced in older mice at baseline (young 27.6 > mature 19.3%, P = 0.01) and during dobutamine infusion (young 53.0 > mature 36.2%, P = 0.005). In the infrarenal aorta, the response (dobutamine - baseline) was reduced in older mice (young 21.9 > mature 13.5%, P = 0.04). DATA CONCLUSION: Dobutamine infusion increases circumferential cyclic strain throughout the arterial tree of mice. This effect is quantifiable using CINE MRI. The results demonstrate that strain prior to and during dobutamine is influenced by anatomical location, sex, and age. LEVEL OF EVIDENCE: 3 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2019;49:69-80.


Subject(s)
Cardiovascular System/diagnostic imaging , Dobutamine/administration & dosage , Heart/diagnostic imaging , Magnetic Resonance Imaging, Cine , Vascular Stiffness , Animals , Aorta/diagnostic imaging , Aorta/drug effects , Biomechanical Phenomena , Female , Heart/drug effects , Heart Rate , Male , Mice , Mice, Inbred C57BL , Sex Factors
10.
Physiol Rep ; 6(16): e13839, 2018 08.
Article in English | MEDLINE | ID: mdl-30155984

ABSTRACT

The cardiovascular system plays a crucial role in thermoregulation. Deep core veins, due to their large size and role in returning blood to the heart, are an important part of this system. The response of veins to increasing core temperature has not been adequately studied in vivo. Our objective was to noninvasively quantify in C57BL/6 mice the response of artery-vein pairs to increases in body temperature. Adult male mice were anesthetized and underwent magnetic resonance imaging. Data were acquired from three colocalized vessel pairs (the neck [carotid/jugular], torso [aorta/inferior vena cava (IVC)], periphery [femoral artery/vein]) at core temperatures of 35, 36, 37, and 38°C. Cross-sectional area increased with increasing temperature for all vessels, excluding the carotid. Average area of the jugular, aorta, femoral artery, and vein linearly increased with temperature (0.10, 0.017, 0.017, and 0.027 mm2 /°C, respectively; P < 0.05). On average, the IVC has the largest venous response for area (18.2%/°C, vs. jugular 9.0 and femoral 10.9%/°C). Increases in core temperature from 35 to 38 °C resulted in an increase in contact length between the aorta/IVC of 29.3% (P = 0.007) and between the femoral artery/vein of 28.0% (P = 0.03). Previously unidentified increases in the IVC area due to increasing core temperature are biologically important because they may affect conductive and convective heat transfer. Vascular response to temperature varied based on location and vessel type. Leveraging noninvasive methodology to quantify vascular responses to temperature could be combined with bioheat modeling to improve understanding of thermoregulation.


Subject(s)
Body Temperature Regulation/physiology , Body Temperature/physiology , Veins/physiology , Animals , Aorta/anatomy & histology , Aorta/diagnostic imaging , Aorta/physiology , Carotid Arteries/anatomy & histology , Carotid Arteries/diagnostic imaging , Carotid Arteries/physiology , Femoral Artery/anatomy & histology , Femoral Artery/diagnostic imaging , Femoral Artery/physiology , Femoral Vein/anatomy & histology , Femoral Vein/diagnostic imaging , Femoral Vein/physiology , Jugular Veins/anatomy & histology , Jugular Veins/diagnostic imaging , Jugular Veins/physiology , Magnetic Resonance Imaging , Male , Mice, Inbred C57BL , Veins/anatomy & histology , Veins/diagnostic imaging , Vena Cava, Inferior/anatomy & histology , Vena Cava, Inferior/diagnostic imaging , Vena Cava, Inferior/physiology
11.
Int J Hyperthermia ; 34(7): 1121-1133, 2018 11.
Article in English | MEDLINE | ID: mdl-29103320

ABSTRACT

PURPOSE: The cardiovascular (CV) system plays a vital role in thermoregulation. To date, the response of core vasculature to increasing core temperature has not been adequately studied in vivo. Our objective was to non-invasively quantify the arterial response in murine models due to increases in body temperature, with a focus on core vessels of the torso and investigate whether responses were dependent on sex or age. METHODS: Male and female, adult and aged mice were anaesthetised and underwent magnetic resonance imaging (MRI). Data were acquired from the circle of Willis (CoW), heart, infrarenal aorta and peripheral arteries at core temperatures of 35, 36, 37 and 38 °C (±0.2 °C). RESULTS: Vessels in the CoW did not change. Ejection fraction decreased and cardiac output (CO) increased with increasing temperature in adult female mice. Cross-sectional area of the aorta increased significantly and linearly with temperature for all groups, but at a diminished rate for aged animals (p < 0.01; male and female: adult, 0.019 and 0.024 mm2/°C; aged, 0.017 and 0.011 mm2/°C). Aged male mice had a diminished response in the periphery (% increase in femoral artery area from 35 to 38 °C, male and female: adult, 67 and 65%; aged, 0.1 and 57%). CONCLUSION: Previously unidentified increases in aortic area due to increasing core temperature are biologically important because they may affect conductive and convective heat transfer. Leveraging non-invasive methodology to quantify sex and age dependent vascular responses due to increasing core temperature could be combined with bioheat modelling in order to improve understanding of thermoregulation.


Subject(s)
Aorta/physiopathology , Adult , Animals , Body Temperature/physiology , Cross-Sectional Studies , Female , Humans , Male , Mice , Middle Aged , Young Adult
12.
Ann Anat ; 214: 43-52, 2017 Nov.
Article in English | MEDLINE | ID: mdl-28865773

ABSTRACT

Although widely used as a preclinical model for studying venous diseases, there is a scarcity of in vivo characterizations of the naïve murine venous system. Additionally, previous studies on naïve veins (ex vivo) have not included the influence of surrounding structures and biomechanical forces. Using MRI, we noninvasively quantified the cross-sectional area, cyclic strain, and circularity of the venous system in young and old, male and female C57BL/6 mice. We investigated the most common venous locations used to perform venous disease research: the common jugular vein, suprarenal inferior vena cava (IVC), infrarenal IVC, common iliac vein, and common femoral vein. Our results elucidate age-dependent changes in venous cross-sectional area, which varied by location. Maximum cyclic strain, a parameter of lumen expansion, showed 10% change across the cardiac cycle, approximately half the magnitude of arteries. Veins demonstrated noncircular shapes, particularly in the core vasculature. The cardiovascular stressor dobutamine had only a small impact on the venous system. Also, our data demonstrate that the peripheral veins tend to decrease in cross-sectional area and circularity with age. Conversely, the IVC tends to increase in size and circularity with age, with males exhibiting larger variability in response to dobutamine compared to females. This work provides a foundation for drawing age and sex comparisons in disease models, and represents the first in vivo characterization of the murine venous system at rest and during the application of a pharmacological exercise surrogate.


Subject(s)
Aging/physiology , Disease Models, Animal , Dobutamine , Vasodilation/drug effects , Veins/physiopathology , Venous Thrombosis/physiopathology , Aging/drug effects , Aging/pathology , Animals , Dose-Response Relationship, Drug , Female , Male , Mice , Mice, Inbred C57BL , Sex Characteristics , Shear Strength/drug effects , Stress, Mechanical , Treatment Outcome , Vasodilator Agents/administration & dosage , Veins/drug effects , Veins/pathology , Venous Thrombosis/chemically induced , Venous Thrombosis/pathology
13.
Langmuir ; 25(1): 422-8, 2009 Jan 06.
Article in English | MEDLINE | ID: mdl-19063643

ABSTRACT

We report small angle neutron scattering (SANS) experiments on two crude oils. Analysis of the high-Q SANS region has probed the asphaltene aggregates in the nanometer length scale. We find that the radius of gyration decreases with increasing temperature. We show that SANS measurements on crude oils give similar aggregate sizes to those found from SANS measurements of asphaltenes redispersed in deuterated toluene. The combined use of SANS and V-SANS on crude oil samples has allowed the determination of the radius of gyration of large scale asphaltene aggregates of approximately 0.45 microm. This has been achieved by the fitting of Beaucage functions over two size regimes. Analysis of the fitted Beaucage functions at very low-Q has shown that the large scale aggregates are not simply made by aggregation of all the smaller nanoaggregates. Instead, they are two different aggregates coexisting.

14.
Magn Reson Imaging ; 25(4): 513-6, 2007 May.
Article in English | MEDLINE | ID: mdl-17466776

ABSTRACT

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.


Subject(s)
Magnetic Resonance Spectroscopy/methods , Statistical Distributions , Algorithms , Fourier Analysis , Polysaccharides, Bacterial/chemistry , Porosity , Rheology/methods , Water/chemistry
15.
Magn Reson Imaging ; 23(2): 363-5, 2005 Feb.
Article in English | MEDLINE | ID: mdl-15833648

ABSTRACT

We measure the probability distribution P(zeta)--the propagator--of molecular displacements on Stokes flow through a pack of microporous glass beads and a carbonate rock. An optimized sampling of q-space is introduced for the measurement of a P(zeta) and its first moment zeta. Our results delineate and provide an understanding of the experimental regimes where background fields and surface relaxation distort the measured propagators.


Subject(s)
Magnetic Resonance Spectroscopy , Porosity , Carbonates/chemistry , Geologic Sediments/chemistry , Glass , Rheology , Surface Properties
16.
J Magn Reson ; 172(1): 31-5, 2005 Jan.
Article in English | MEDLINE | ID: mdl-15589405

ABSTRACT

We present a one-scan method for determining fluid flow velocity within a few milliseconds in the presence of a static field gradient, and without the need of multiple scans. A few RF-pulses populate a series of coherence pathways, each of which exhibits a phase shift that is proportional to fluid velocity. These coherence pathways produce spin echoes separated in the time domain, thus eliminating the need for phase cycling.


Subject(s)
Magnetic Resonance Spectroscopy/methods , Rheology , Models, Theoretical , Radio Waves , Signal Processing, Computer-Assisted
17.
Phys Rev Lett ; 89(25): 254501, 2002 Dec 16.
Article in English | MEDLINE | ID: mdl-12484890

ABSTRACT

The propagator for molecular displacements P(zeta, t) and its first three cumulants were measured for Stokes flow in monodisperse bead packs with different sphere sizes d and molecular diffusion coefficients D(m). We systematically varied the normalized mean displacement /d and diffusion length L(D)=sqrt[2D(m)t]/d. The experimental results map onto each other with this scaling. For L(D)/d<0.2 the propagator remains non-Gaussian, and thus an advection diffusion equation is not obeyed, for mean displacements measured up to >10d. A Gaussian shape is approached for large mean displacements when L(D)>0.3d.

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