47 research outputs found
Random Splitting of Point Vortex Flows
We consider a stochastic version of the point vortex system, in which the
fluid velocity advects single vortices intermittently for small random times.
Such system converges to the deterministic point vortex dynamics as the rate at
which single components of the vector field are randomly switched diverges, and
therefore it provides an alternative discretization of 2D Euler equations. The
random vortex system we introduce preserves microcanonical statistical
ensembles of the point vortex system, hence constituting a simpler alternative
to the latter in the statistical mechanics approach to 2D turbulence.Comment: 9 pages, 0 figure
Random Splitting of Fluid Models: Ergodicity and Convergence
We introduce a family of stochastic models motivated by the study of
nonequilibrium steady states of fluid equations. These models decompose the
deterministic dynamics of interest into fundamental building blocks, i.e.,
minimal vector fields preserving some fundamental aspects of the original
dynamics. Randomness is injected by sequentially following each vector field
for a random amount of time. We show under general assumptions that these
random dynamics possess a unique invariant measure and converge almost surely
to the original, deterministic model in the small noise limit. We apply our
construction to the Lorenz-96 equations, often used in studies of chaos and
data assimilation, and Galerkin approximations of the 2D Euler and
Navier-Stokes equations. An interesting feature of the models developed is that
they apply directly to the conservative dynamics and not just those with
excitation and dissipation
Telemetric Blood Pressure Assessment in Angiotensin II-Infused ApoE\u3csup\u3e-/-\u3c/sup\u3e Mice: 28 Day Natural History and Comparison to Tail-Cuff Measurements
Abdominal aortic aneurysm (AAA) is a disease of the aortic wall, which can progress to catastrophic rupture. Assessment of mechanical characteristics of AAA, such as aortic distensibility, may provide important insights to help identify at-risk patients and understand disease progression. While the majority of studies on this topic have focused on retrospective patient data, recent studies have used mouse models of AAA to prospectively evaluate the evolution of aortic mechanics. Quantification of aortic distensibility requires accurate measurement of arterial blood pressure, particularly pulse pressure, which is challenging to perform accurately in murine models. We hypothesized that volume/pressure tail-cuff measurements of arterial pulse pressure in anesthetized mice would have sufficient accuracy to enable calculations of aortic distensibility with minimal error. Telemetry devices and osmotic mini-pumps filled with saline or angiotensin-II were surgically implanted in male apolipoprotein-E deficient (ApoE-/-) mice. Blood pressure in the aortic arch was measured continuously via telemetry. In addition, simultaneous blood pressure measurements with a volume/pressure tail-cuff system were performed under anesthesia at specific intervals to assess agreement between techniques. Compared to controls, mice infused with angiotensin-II had an overall statistically significant increase in systolic pressure, with no overall difference in pulse pressure; however, pulse pressure did increase significantly with time. Systolic measurements agreed well between telemetry and tail-cuff (coefficient of variation = 10%), but agreement of pulse pressure was weak (20%). In fact, group-averaged pulse pressure from telemetry was a better predictor of a subject\u27s pulse pressure on a given day than a simultaneous tail-cuff measurement. Furthermore, these approximations introduced acceptable errors (15.1 ± 12.8%) into the calculation of aortic distensibility. Contrary to our hypothesis, we conclude that tail-cuff measures of arterial pulse pressure have limited accuracy. Future studies of aneurysm mechanics using the ApoE-/-/angiotensin-II model would be better in assuming pulse pressure profiles consistent with our telemetry findings instead of attempting to measure pulse pressure in individual mice
Characterizing the Temporal Evolution of Altered Cardiac Mechanics in Diet-Induced Obese Mice Using Cine DENSE CMR
Background
Obesity and metabolic syndrome are associated with increased risk of cardiovascular disease. Research suggests that altered cardiac mechanics (i.e., reduced strains, torsion, and synchrony of contraction) are present in obesity; yet, the causes of this mechanical dysfunction and its relationship to other sequelae of obesity (e.g., hypertension and elevated blood glucose) are not well understood. We hypothesize that diet-induced obesity in mice leads to reductions in measures of left ventricular (LV) mechanics, which develop in acute response to the onset of hyperglycemia, hypertension, and ventricular remodeling.
Methods
Twenty 4-week-old C57BL/6J mice were randomized (n = 10 per group) to either a high-fat (60% kcal from fat) or sucrose-matched low-fat (10% kcal from fat) diet for 28 weeks. After 4 weeks and every 6 weeks thereafter, LV mechanics were quantified using cine displacement encoding with stimulated echoes (DENSE) on a 7T ClinScan MRI (Bruker, Ettlingen, Germany) with a 4-element phased array cardiac coil. Three short-axis and two long-axis slices were acquired with 13-20 frames per cardiac cycle. Semi-automated post-processing was performed using custom software in MATLAB (Mathworks, Natick, MA). Additionally, systolic blood pressure (via tail cuff measurement) and fasting blood glucose were assessed every 4 weeks on staggered schedules.
Results
Mice on the high-fat diet became obese relative to the low-fat controls (49.9 vs. 29.2 g, respectively, by week 28;). Fasting blood glucose was elevated in the high-fat group (202 vs. 112 mg/dL; p \u3c 0.05) starting from the earliest measurement (week 7 on diet), whereas significant differences in LV mass (88 vs. 79 mg) and systolic blood pressure (172 vs. 162 mmHg) developed much later (weeks 22 and 25 on diet, respectively). Significant reductions in peak LV radial (15%) and circumferential (8%) strains and reduced contractile synchrony were detected in the high-fat group for the first time in week 28. A 10% reduction in peak torsion was also observed at that time, but did not reach statistical significance (p = 0.075). There were no differences in LV cavity volumes or ejection fraction.
Conclusions
Diet-induced obesity in mice is associated with reduced left ventricular mechanics. This dysfunction develops long after the manifestation of hyperglycemia in this model, which suggests that chronic alterations in glucose/insulin levels and/or signaling may contribute more to cardiac contractile dysfunction than acute elevations. Late development of concentric ventricular hypertrophy and hypertension prior to suppressed cardiac mechanics also suggests an important role of these processes in the reduced ventricular function
Reproducibility of cine displacement encoding with stimulated echoes (DENSE) cardiovascular magnetic resonance for measuring left ventricular strains, torsion, and synchrony in mice
BACKGROUND: Advanced measures of cardiac function are increasingly important to clinical assessment due to their superior diagnostic and predictive capabilities. Cine DENSE cardiovascular magnetic resonance (CMR) is ideal for quantifying advanced measures of cardiac function based on its high spatial resolution and streamlined post-processing. While many studies have utilized cine DENSE in both humans and small-animal models, the inter-test and inter-observer reproducibility for quantification of advanced cardiac function in mice has not been evaluated. This represents a critical knowledge gap for both understanding the capabilities of this technique and for the design of future experiments. We hypothesized that cine DENSE CMR would show excellent inter-test and inter-observer reproducibility for advanced measures of left ventricular (LV) function in mice.
METHODS: Five normal mice (C57BL/6) and four mice with depressed cardiac function (diet-induced obesity) were imaged twice, two days apart, on a 7T ClinScan MR system. Images were acquired with 15-20 frames per cardiac cycle in three short-axis (basal, mid, apical) and two long-axis orientations (4-chamber and 2-chamber). LV strain, twist, torsion, and measures of synchrony were quantified. Images from both days were analyzed by one observer to quantify inter-test reproducibility, while inter-observer reproducibility was assessed by a second observer\u27s analysis of day-1 images. The coefficient of variation (CoV) was used to quantify reproducibility.
RESULTS: LV strains and torsion were highly reproducible on both inter-observer and inter-test bases with CoVs ≤ 15%, and inter-observer reproducibility was generally better than inter-test reproducibility. However, end-systolic twist angles showed much higher variance, likely due to the sensitivity of slice location within the sharp longitudinal gradient in twist angle. Measures of synchrony including the circumferential (CURE) and radial (RURE) uniformity of strain indices, showed excellent reproducibility with CoVs of 1% and 3%, respectively. Finally, peak measures (e.g., strains) were generally more reproducible than the corresponding rates of change (e.g., strain rate).
CONCLUSIONS: Cine DENSE CMR is a highly reproducible technique for quantification of advanced measures of left ventricular cardiac function in mice including strains, torsion and measures of synchrony. However, myocardial twist angles are not reproducible and future studies should instead report torsion
Obesity Reduces Left Ventricular Strains, Torsion, and Synchrony in Mouse Models: A Cine Displacement Encoding with Stimulated Echoes (DENSE) Cardiovascular Magnetic Resonance Study
BACKGROUND: Obesity affects a third of adults in the US and results in an increased risk of cardiovascular mortality. While the mechanisms underlying this increased risk are not well understood, animal models of obesity have shown direct effects on the heart such as steatosis and fibrosis, which may affect cardiac function. However, the effect of obesity on cardiac function in animal models is not well-defined. We hypothesized that diet-induced obesity in mice reduces strain, torsion, and synchrony in the left ventricle (LV).
METHODS: Ten 12-week-old C57BL/6 J mice were randomized to a high-fat or low-fat diet. After 5 months on the diet, mice were imaged with a 7 T ClinScan using a cine DENSE protocol. Three short-axis and two long-axis slices were acquired for quantification of strains, torsion and synchrony in the left ventricle.
RESULTS: Left ventricular mass was increased by 15% (p = 0.032) with no change in volumes or ejection fraction. Subepicardial strain was lower in the obese mice with a 40% reduction in circumferential strain (p = 0.008) a 53% reduction in radial strain (p = 0.032) and a trend towards a 19% reduction in longitudinal strain (p = 0.056). By contrast, subendocardial strain was modestly reduced in the obese mice in the circumferential direction by 12% (p = 0.028), and no different in the radial (p = 0.690) or longitudinal (p = 0.602) directions. Peak torsion was reduced by 34% (p = 0.028). Synchrony of contraction was also reduced (p = 0.032) with a time delay in the septal-to-lateral direction.
CONCLUSIONS: Diet-induced obesity reduces left ventricular strains and torsion in mice. Reductions in cardiac strain are mostly limited to the subepicardium, with relative preservation of function in the subendocardium. Diet-induced obesity also leads to reduced synchrony of contraction and hypertrophy in mouse models
Left Ventricular Mechanical Dysfunction in Diet-Induced Obese Mice Is Exacerbated During Inotropic Stress: A Cine DENSE Cardiovascular Magnetic Resonance Study
BACKGROUND: Obesity is a risk factor for cardiovascular disease. There is evidence of impaired left ventricular (LV) function associated with obesity, which may relate to cardiovascular mortality, but some studies have reported no dysfunction. Ventricular function data are generally acquired under resting conditions, which could mask subtle differences and potentially contribute to these contradictory findings. Furthermore, abnormal ventricular mechanics (strains, strain rates, and torsion) may manifest prior to global changes in cardiac function (i.e., ejection fraction) and may therefore represent more sensitive markers of cardiovascular disease. This study evaluated LV mechanics under both resting and stress conditions with the hypothesis that the LV mechanical dysfunction associated with obesity is exacerbated with stress and manifested at earlier stages of disease compared to baseline.
METHODS: C57BL/6J mice were randomized to a high-fat or control diet (60 %, 10 % kcal from fat, respectively) for varying time intervals (n = 7 - 10 subjects per group per time point, 100 total; 4 - 55 weeks on diet). LV mechanics were quantified under baseline (resting) and/or stress conditions (40 μg/kg/min continuous infusion of dobutamine) using cine displacement encoding with stimulated echoes (DENSE) with 7.4 ms temporal resolution on a 7 T Bruker ClinScan. Peak strain, systolic strain rates, and torsion were quantified. A linear mixed model was used with Benjamini-Hochberg adjustments for multiple comparisons.
RESULTS: Reductions in LV peak longitudinal strain at baseline were first observed in the obese group after 42 weeks, with no differences in systolic strain rates or torsion. Conversely, reductions in longitudinal strain and circumferential and radial strain rates were seen under inotropic stress conditions after only 22 weeks on diet. Furthermore, stress cardiovascular magnetic resonance (CMR) evaluation revealed supranormal values of LV radial strain and torsion in the obese group early on diet, followed by later deficits.
CONCLUSIONS: Differences in left ventricular mechanics in obese mice are exacerbated under stress conditions. Stress CMR demonstrated a broader array of mechanical dysfunction and revealed these differences at earlier time points. Thus, it may be important to evaluate cardiac function in the setting of obesity under stress conditions to fully elucidate the presence of ventricular dysfunction
Simplified Post Processing of Cine DENSE Cardiovascular Magnetic Resonance for Quantification of Cardiac Mechanics
BACKGROUND: Cardiovascular magnetic resonance using displacement encoding with stimulated echoes (DENSE) is capable of assessing advanced measures of cardiac mechanics such as strain and torsion. A potential hurdle to widespread clinical adoption of DENSE is the time required to manually segment the myocardium during post-processing of the images. To overcome this hurdle, we proposed a radical approach in which only three contours per image slice are required for post-processing (instead of the typical 30-40 contours per image slice). We hypothesized that peak left ventricular circumferential, longitudinal and radial strains and torsion could be accurately quantified using this simplified analysis.
METHODS AND RESULTS: We tested our hypothesis on a large multi-institutional dataset consisting of 541 DENSE image slices from 135 mice and 234 DENSE image slices from 62 humans. We compared measures of cardiac mechanics derived from the simplified post-processing to those derived from original post-processing utilizing the full set of 30-40 manually-defined contours per image slice. Accuracy was assessed with Bland-Altman limits of agreement and summarized with a modified coefficient of variation. The simplified technique showed high accuracy with all coefficients of variation less than 10% in humans and 6% in mice. The accuracy of the simplified technique was also superior to two previously published semi-automated analysis techniques for DENSE post-processing.
CONCLUSIONS: Accurate measures of cardiac mechanics can be derived from DENSE cardiac magnetic resonance in both humans and mice using a simplified technique to reduce post-processing time by approximately 94%. These findings demonstrate that quantifying cardiac mechanics from DENSE data is simple enough to be integrated into the clinical workflow
Reproducibility of cine displacement encoding with stimulated echoes (DENSE) cardiovascular magnetic resonance for measuring left ventricular strains, torsion, and synchrony in mice
BACKGROUND: Advanced measures of cardiac function are increasingly important to clinical assessment due to their superior diagnostic and predictive capabilities. Cine DENSE cardiovascular magnetic resonance (CMR) is ideal for quantifying advanced measures of cardiac function based on its high spatial resolution and streamlined post-processing. While many studies have utilized cine DENSE in both humans and small-animal models, the inter-test and inter-observer reproducibility for quantification of advanced cardiac function in mice has not been evaluated. This represents a critical knowledge gap for both understanding the capabilities of this technique and for the design of future experiments. We hypothesized that cine DENSE CMR would show excellent inter-test and inter-observer reproducibility for advanced measures of left ventricular (LV) function in mice. METHODS: Five normal mice (C57BL/6) and four mice with depressed cardiac function (diet-induced obesity) were imaged twice, two days apart, on a 7T ClinScan MR system. Images were acquired with 15–20 frames per cardiac cycle in three short-axis (basal, mid, apical) and two long-axis orientations (4-chamber and 2-chamber). LV strain, twist, torsion, and measures of synchrony were quantified. Images from both days were analyzed by one observer to quantify inter-test reproducibility, while inter-observer reproducibility was assessed by a second observer’s analysis of day-1 images. The coefficient of variation (CoV) was used to quantify reproducibility. RESULTS: LV strains and torsion were highly reproducible on both inter-observer and inter-test bases with CoVs ≤ 15%, and inter-observer reproducibility was generally better than inter-test reproducibility. However, end-systolic twist angles showed much higher variance, likely due to the sensitivity of slice location within the sharp longitudinal gradient in twist angle. Measures of synchrony including the circumferential (CURE) and radial (RURE) uniformity of strain indices, showed excellent reproducibility with CoVs of 1% and 3%, respectively. Finally, peak measures (e.g., strains) were generally more reproducible than the corresponding rates of change (e.g., strain rate). CONCLUSIONS: Cine DENSE CMR is a highly reproducible technique for quantification of advanced measures of left ventricular cardiac function in mice including strains, torsion and measures of synchrony. However, myocardial twist angles are not reproducible and future studies should instead report torsion
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Religious transformations in the Middle Ages: towards a new archaeological agenda
The study of religious change in Europe between the collapse of the Roman Empire and the Reformation forms one of the cornerstones of medieval archaeology but has been riven by period, denominational and geographical divisions. This paper lays the groundwork for a fundamental rethink of archaeological approaches to medieval religions, by adopting a holistic framework that places Christian, pagan, Islamic and Jewish case studies of religious transformation in a long-term, comparative perspective. Focused around the analytical themes of ‘hybridity and resilience’ and ‘tempo and trajectories’, our approach shifts attention away from the singularities of national narratives of religious conversion towards a deeper understanding of how religious beliefs, practices and identity were renegotiated by medieval people in their daily lives