Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats

We consider a spherically symmetric line element which admits either a black hole geometry or a wormhole geometry and show that in both cases the apparent horizon or the wormhole throat is partially characterized by the zero set of a single curvature invariant. The detection of the apparent horizon by this invariant is consistent with the geometric horizon detection conjectures and implies that it is a geometric horizon of the black hole, while the detection of the wormhole throat presents a conceptual problem for the conjectures. To distinguish between these surfaces, we determine a set of curvature invariants that fully characterize the apparent horizon and wormhole throat. Motivated by this result, we introduce the concept of a geometric surface as a generalization of a geometric horizon and extend the geometric horizon detection conjectures to geometric surfaces. As an application, we employ curvature invariants to characterize three important surfaces of the line element introduced by Simpson, Martin-Moruno, and Visser, which describes transitions between regular Vaidya black holes, traversable wormholes, and black bounces.acceptedVersio

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

Curvature Invariants for the Alcubierre and Nat\'ario Warp Drives

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natario warp drives at a constant velocity.Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes such as warp drives. Warp drives are the theoretical solutions to Einstein's field equations that allow the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter's unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natario warp drive do not contain a wake or a constant curvature indicating that these are unique features of the accelerating Natario warp drive.Comment: 41 Pages, 15 figure

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

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. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12968-015-0180-7) contains supplementary material, which is available to authorized users