Steady-state Susceptibility Research Articles

Steady-state susceptibility in continuous phase transitions of dissipative systems

In this work, we explore the critical behaviors of fidelity susceptibility and trace distance susceptibility associated to the steady states of dissipative systems at continuous phase transitions. We investigate on two typical models, one is the dissipative spin-1/2 XYZ model on two-dimensional square lattice and the other is a driven-dissipative Kerr oscillator. We find that the susceptibilities of fidelity and trace distance exhabit singular behaviors near the critical points of phase transitions in both models. The critical points, in thermodynamic limit, extracted from the scalings of the critical controlling parameters to the system size or nonlinearity agree well with the existed results.

Non-Invasive Evaluation of Cerebral Microvasculature Using Pre-Clinical MRI: Principles, Advantages and Limitations.

Alterations to the cerebral microcirculation have been recognized to play a crucial role in the development of neurodegenerative disorders. However, the exact role of the microvascular alterations in the pathophysiological mechanisms often remains poorly understood. The early detection of changes in microcirculation and cerebral blood flow (CBF) can be used to get a better understanding of underlying disease mechanisms. This could be an important step towards the development of new treatment approaches. Animal models allow for the study of the disease mechanism at several stages of development, before the onset of clinical symptoms, and the verification with invasive imaging techniques. Specifically, pre-clinical magnetic resonance imaging (MRI) is an important tool for the development and validation of MRI sequences under clinically relevant conditions. This article reviews MRI strategies providing indirect non-invasive measurements of microvascular changes in the rodent brain that can be used for early detection and characterization of neurodegenerative disorders. The perfusion MRI techniques: Dynamic Contrast Enhanced (DCE), Dynamic Susceptibility Contrast Enhanced (DSC) and Arterial Spin Labeling (ASL), will be discussed, followed by less established imaging strategies used to analyze the cerebral microcirculation: Intravoxel Incoherent Motion (IVIM), Vascular Space Occupancy (VASO), Steady-State Susceptibility Contrast (SSC), Vessel size imaging, SAGE-based DSC, Phase Contrast Flow (PC) Quantitative Susceptibility Mapping (QSM) and quantitative Blood-Oxygenation-Level-Dependent (qBOLD). We will emphasize the advantages and limitations of each strategy, in particular on applications for high-field MRI in the rodent’s brain.

Vasculature-specific MRI reveals differential anti-angiogenic effects of a biomimetic peptide in an orthotopic breast cancer model.

Translational vasculature-specific MRI biomarkers were used to measure the effects of a novel anti-angiogenic biomimetic peptide in an orthotopic MDA-MB-231 human triple-negative breast cancer model at an early growth stage. In vivo diffusion-weighted and steady-state susceptibility contrast (SSC) MRI was performed pre-treatment and 2 weeks post-treatment in tumor volume-matched treatment and control groups (n = 5/group). Treatment response was measured by changes in tumor volume; baseline transverse relaxation time (T2); apparent diffusion coefficient (ADC); and SSC-MRI metrics of blood volume, vessel size, and vessel density. These vasculature-specific SSC-MRI biomarkers were compared to the more conventional, non-vascular biomarkers (tumor growth, ADC, and T2) in terms of their sensitivity to anti-angiogenic treatment response. After 2 weeks of peptide treatment, tumor growth inhibition was evident but not yet significant, and the changes in ADC or T2 were not significantly different between treated and control groups. In contrast, the vascular MRI biomarkers revealed a significant anti-angiogenic response to the peptide after 2 weeks—blood volume and vessel size decreased, and vessel density increased in treated tumors; the opposite was seen in control tumors. The MRI results were validated with histology—H&E staining showed no difference in tumor viability between groups, while peptide-treated tumors exhibited decreased vascularity. These results indicate that translational SSC-MRI biomarkers are able to detect the differential effects of anti-angiogenic therapy on the tumor vasculature before significant tumor growth inhibition or changes in tumor viability.

Ferumoxytol administration does not alter infarct volume or the inflammatory response to stroke in mice

Ferumoxytol is an ultrasmall superparamagnetic iron oxide (USPIO) nanoparticle that is FDA-approved as an intravenous iron replacement therapy for the treatment of iron deficiency anemia in patients with chronic kidney disease. Ferumoxytol has also been used as a contrast agent for cerebral blood volume mapping by magnetic resonance imaging (MRI), which suggests it could be used for imaging hemodynamic abnormalities after stroke. However, circulating macrophages can internalize USPIOs, and recent data indicate that the accumulation of iron in macrophages can lead them to adopt the M1 pro-inflammatory phenotype. Therefore, the uptake of intravenously administered iron particles by circulating macrophages that home to the stroke core could potentially alter the inflammatory response to stroke. To test this possibility in vivo we administered a dose of ferumoxytol previously used to obtain cerebral blood volume maps in healthy humans by steady-state susceptibility contrast (SSC) MRI to BALB/cJ mice 48h after stroke and examined cytokine levels, microglial/macrophage activation, and lesion volume in the brain 5 days later. Treatment with ferumoxytol did not lead to any differences in these parameters. These data indicate that the use of ferumoxytol as a contrast agent for brain imaging after stroke does not alter the inflammatory response to stroke in mice, and is therefore unlikely to do so in human subjects.

Assessing breast cancer angiogenesis in vivo: which susceptibility contrast MRI biomarkers are relevant?

There is an impending need for noninvasive biomarkers of breast cancer angiogenesis to evaluate the efficacy of new anti-angiogenic therapies in vivo. The purpose of this study was to systematically evaluate the sensitivity of in vivo steady-state susceptibility contrast-MRI biomarkers of angiogenesis in a human breast cancer model. Orthotopic MDA-MB-231 human breast cancer xenografts were imaged by steady-state susceptibility contrast-MRI at post-inoculation week 3 and post-inoculation week 5, followed by ex vivo whole tumor 3D micro-CT angiography. "Absolute" (i.e., measures of vascular morphology in appropriate units) and "relative" (i.e., proportional to measures of vascular morphology) MRI biomarkers of tumor blood volume, vessel size, and vessel density were computed and their ability to predict the corresponding micro-CT analogs assessed using cross-validation analysis. All MRI biomarkers significantly correlated with their micro-CT analogs and were sensitive to the micro-CT-measured decreases in tumor blood volume and vessel density from post-inoculation week 3 to post-inoculation week 5. However, cross-validation analysis revealed there was no significant difference between the predictive accuracy of "absolute" and "relative" biomarkers. As "relative" biomarkers are more easily computed from steady-state susceptibility contrast-MRI (i.e., without additional MRI measurements) than "absolute" biomarkers, it makes them promising candidates for assessing breast cancer angiogenesis in vivo.

Vessel size index measurements in a rat model of glioma: comparison of the dynamic (Gd) and steady‐state (iron‐oxide) susceptibility contrast MRI approaches

Vessel size index (VSI), a parameter related to the distribution of vessel diameters, may be estimated using two MRI approaches: (i) dynamic susceptibility contrast (DSC) MRI following the injection of a bolus of Gd-chelate. This technique is routinely applied in the clinic to assess intracranial tissue perfusion in patients; (ii) steady-state susceptibility contrast with USPIO contrast agents, which is considered here as the standard method. Such agents are not available for human yet and the steady-state approach is currently limited to animal studies. The aim is to compare VSI estimates obtained with these two approaches on rats bearing C6 glioma (n = 7). In a first session, VSI was estimated from two consecutive injections of Gd-Chelate (Gd(1) and Gd(2)). In a second session (4 hours later), VSI was estimated using USPIO. Our findings indicate that both approaches yield comparable VSI estimates both in contralateral (VSI{USPIO} = 7.5 ± 2.0 µm, VSI{Gd(1)} = 6.5 ± 0.7 µm) and in brain tumour tissues (VSI{USPIO} = 19.4 ± 7.1 µm, VSI{Gd(1)} = 16.6 ± 4.5 µm). We also observed that, in the presence of BBB leakage (as it occurs typically in brain tumours), applying a preload of Gd-chelate improves the VSI estimate with the DSC approach both in contralateral (VSI{Gd(2)} = 7.1 ± 0.4 µm) and in brain tumour tissues (VSI{Gd(2)} = 18.5 ± 4.3 µm) but is not mandatory. VSI estimates do not appear to be sensitive to T(1) changes related to Gd extravasation. These results suggest that robust VSI estimates may be obtained in patients at 3 T or higher magnetic fields with the DSC approach.

In vivo validation of MRI vessel caliber index measurement methods with intravital optical microscopy in a U87 mouse brain tumor model

The vessel caliber index (VCI), a magnetic resonance imaging biomarker of the average blood vessel diameter, is increasingly being used as a tool for assessing tumor angiogenesis and response to antiangiogenic therapy. However, although the VCI has been correlated with histological vessel diameters, good quantitative agreement with histology has been lacking. In addition, no VCI validation studies have been performed in vivo where the structural deformations frequently associated with histological tissue preparation are not present. This study employs intravital optical microscopy (IVM) measurements of cerebral blood vessel diameters in a mouse orthotopic glioma model to provide the first such in vivo validation. Two VCI correlation models, both a linear and a 3/2-power dependence on the DeltaR2*/DeltaR2 ratio, were compared with the IVM data. The linear VCI model, determined from steady-state susceptibility contrast (SSC) images, was found to be in excellent quantitative agreement with the intravitally determined VCI for separate tumor size matched groups of mice. In addition, preliminary data indicate that the VCI is independent of whether a dynamic susceptibility contrast or SSC measurement method is used.

NON-LINEAR INTERACTION OF TWO INTENSE FIELDS WITH A THREE-LEVEL ATOMIC SYSTEM

The interaction between two intense fields with a closed three-level atomic system in the cascade configuration is considered. We derive the steady-state expressions for the field-induced susceptibilities which are valid for all field strengths for the two fields. In particular, we show that each field influences the steady-state susceptibility and absorption experienced by the other field.

Characteristics of Ultrasmall Superparamagnetic Iron Oxides in Patients with Brain Tumors

The aim of this study was to evaluate the characteristics of an ultrasmall superparamagnetic iron oxides (USPIO) agent in patients with brain tumors and to correlate changes on MRI with histopathologic data collected systematically in all patients. Nine patients with brain tumors were imaged before and 24 hr after administration of a USPIO at a dose of 2.6 mg Fe/kg. Analysis of MR images included qualitative and quantitative comparison of the USPIO and gadolinium enhancement of brain tumors. Brain surgery was performed 25-112 hr after administration of the USPIO. The histopathologic workup included iron histochemistry with diaminobenzidine (DAB)-enhanced Perls stain. In seven of nine patients, USPIO-related changes of signal intensity were observed in gadolinium-enhancing brain tumors on T1- and T2*-weighted sequences. The difference in signal intensity on T1-weighted USPIO series was 40.1% +/- 26.7% (mean +/- SD). On T2*-weighted USPIO series, the difference in signal intensity was -33.1% +/- 18.4% in solid tumor parts. Areas of suspected radiation necrosis did not enhance in three patients with prior radiation therapy. Iron histochemistry revealed the presence of iron deposits in macrophages in two patients. USPIO agents will not replace gadolinium in the workup of patients with brain tumors. Our findings suggest that USPIO agents seem to offer complementary information and may help to differentiate between brain tumors and areas of radiation necrosis. Signal intensity changes on T2*-weighted images might be related to the blood pool properties of the agent, possibly reflecting steady-state susceptibility effects.

Mapping cyclic change of regional myocardial blood volume using steady-state susceptibility effect of iron oxide nanoparticles.

To demonstrate an in vivo magnetic resonance imaging (MRI) technique that maps the cyclic change of regional myocardial blood volume (MBV) during the cardiac cycle. The method is based on the dominant T(2)* shortening effect of iron oxide nanoparticle-induced magnetic susceptibility perturbation in myocardium in the steady state. The technique was demonstrated in vivo with normal mouse hearts at 9.4 T. The regional MBV maps in left ventricular myocardium were computed from the steady-state pre- and post-monocrystalline iron oxide nanoparticle (MION) gradient echo (GE) cine images. Cyclic changes of MBV in normal mice were analyzed quantitatively in different transmural and angular locations. High-resolution MBV maps at various cardiac points were obtained. The study showed a general regional MBV decrease from end-diastole (ED) to end-systole (ES). Percentage reductions were 18.2 +/- 6.6%, P < 0.03 in the lateral wall and 24.7 +/- 3.1%, P < 0.0002 in the interventricular septum. The heterogeneous characteristics of MBV transmural distribution were also reported. The steady-state susceptibility effect of intravascular superparamagnetic contrast agent (CA) can be used to map the cyclic change of regional MBV. This imaging approach is relatively simple and may provide a new perspective for functional assessment of the microvasculature in myocardium.

The Effects of Sustained Hyperventilation on Regional Cerebral Blood Volume in Thiopental-Anesthetized Rats

Sustained hyperventilation has a time-limited effect on cerebrovascular dynamics. We investigated whether this effect was similar among brain regions by measuring regional cerebral blood volume (CBV) with steady-state susceptibility contrast magnetic resonance imaging during 3 h of hyperventilation. Regional CBV was determined in nine thiopental-anesthetized, mechanically-ventilated rats every 30 min in the dorsoparietal neocortex, the corpus striatum, and the cerebellum. The corpus striatum was the only brain region showing a stable reduction in CBV during the hypocapnic episode (PaCO(2), 24 +/- 3 mm Hg). In contrast, neocortex and, to a lesser extent, cerebellum exhibited a progressive return toward normal values despite continued hypocapnia. No evidence of a rebound in CBV was found on return to normal ventilation in the three brain regions. We conclude that sustained hyperventilation can lead to an uneven change in the reduction of CBV, possibly because of differences of brain vessels in their sensitivity to extracellular pH. Our results in neocortex confirm the transient effect of sustained hyperventilation on cerebral hemodynamics. Sustained hyperventilation has a transient effect in decreasing cerebral blood volume (CBV). Using susceptibility contrast magnetic resonance imaging in thiopental-anesthetized rats, we found differences between brain regions in their transient CBV response to sustained hyperventilation.

Is all perfusion-weighted magnetic resonance imaging for stroke equal? The temporal evolution of multiple hemodynamic parameters after focal ischemia in rats correlated with evidence of infarction.

Although perfusion-weighted imaging techniques are increasingly used to study stroke, no particular hemodynamic variable has emerged as a standard marker for accumulated ischemic damage. To better characterize the hemodynamic signature of infarction. the authors have assessed the severity and temporal evolution of ischemic hemodynamics in a middle cerebral artery occlusion model in the rat. Cerebral blood flow (CBF) and total and microvascular cerebral blood volume (CBV) changes were measured with arterial spin labeling and steady-state susceptibility contrast magnetic resonance imaging (MRI), respectively, and analyzed in regions corresponding to infarcted and spared ipsilateral tissue, based on 2,3,5-triphenyltetrazolium chloride histology sections after 24 hours ischemia. Spin echo susceptibility contrast was used to measure microvascular-weighted CBV, which had a maximum sensitivity for vessels with radii between 4 and 30 microm. Serial measurements between 1 and 3 hours after occlusion showed no change in CBF (22 +/- 20% of contralateral, mean +/- SD) or in total CBV (78 +/- 13% of contralateral) in regions destined to infarct. However, microvascular CBV progressively declined from 72 +/- 5% to 64 +/- 11% (P < 0.01) during this same period. Microvascular CBV changes with time were entirely due to decreases in subcortical infarcted zones (from 73 +/- 9% to 57 +/- 14%. P < 0.001) without changes in the cortical infarcted territory. The hemodynamic variables showed differences in magnitude and temporal response, and these changes varied based on histologic outcome and brain architecture. Such factors should be considered when designing imaging studies for human stroke.

Regional cerebral blood volume response to hypocapnia using susceptibility contrast MRI.

We used steady-state susceptibility contrast MRI to evaluate the regional cerebral blood volume (rCBV) response to hypocapnia in anesthetised rats. The rCBV was determined in the dorsoparietal neocortex, the corpus striatum, the cerebellum, as well as blood volume in extracerebral tissue (group 1). In addition, we used laser-Doppler flow (LDF) measurements in the left dorsoparietal neocortex (group 2), to correlate changes in CBV and in cerebral blood flow. Baseline values, expressed as a percentage of blood volume in each voxel, were higher in the brain regions than in extracerebral tissue. Hypocapnia (P(a)CO(2) approximately 25 mmHg) resulted in a significant decrease in CBV in the cerebellum (-17 +/- 9%), in the corpus striatum (-15 +/- 6%) and in the neocortex (-12 +/- 7%), compared to the normocapnic CBV values (group 1). These changes were in good agreement with the values obtained using alternative techniques. No significant changes in blood volume were found in extracerebral tissue. The CBV changes were reversed during the recovery period. In the left dorsoparietal neocortex, the reduction in LDF (group 2) induced by hypocapnia (-21 +/- 8%) was in accordance with the values predicted by the Poiseuille's law. We conclude that rCBV changes during CO(2) manipulation can be accurately measured by susceptibility contrast MRI. Abbreviations used: ANOVA analysis of variance CBF cerebral blood flow CBV cerebral blood volume CPMG Carr-Purcell-Meiboom-Gill FiO(2) fractional inspired oxygen ICP intracranial pressure LDF laser-Doppler flow MABP mean arterial blood pressure MRI magnetic resonance imaging MTT mean transit time PaCO(2) arterial partial pressure of carbon dioxide PaO(2) arterial partial pressure of oxygen PET positron emission tomography rCBV regional cerebral blood volume SPECT single-photon emission computed tomography

Cerebrovascular dynamics of autoregulation and hypoperfusion. An MRI study of CBF and changes in total and microvascular cerebral blood volume during hemorrhagic hypotension.

To determine how cerebral blood flow (CBF), total and microvascular cerebral blood volume (CBV), and blood oxygenation level-dependent (BOLD) contrast change during autoregulation and hypotension using hemodynamic MRI. Using arterial spin labeling and steady-state susceptibility contrast, we measured CBF and changes in both total and microvascular CBV during hemorrhagic hypotension in the rat (n=9). We observed CBF autoregulation for mean arterial blood pressure (MABP) between 50 and 140 mm Hg, at which average CBF was 1.27+/-0.44 mL. g(-1). min(-1) (mean+/-SD). During autoregulation, total and microvascular CBV changes were small and not significantly different from CBF changes. Consistent with this, no significant BOLD changes were observed. For MABP between 10 and 40 mm Hg, total CBV in the striatum increased slightly (+7+/-12%, P<0.05) whereas microvascular CBV decreased (-15+/-17%, P<0.01); on the cortical surface, total CBV increases were larger (+21+/-18%, P<0.01) and microvascular CBV was unchanged (3+/-22%, P>0.05). With severe hypotension, both total and microvascular CBV decreased significantly. Over the entire range of graded global hypoperfusion, there were increases in the CBV/CBF ratio. Parenchymal CBV changes are smaller than those of previous reports but are consistent with the small arteriolar fraction of total blood volume. Such measurements allow a framework for understanding effective compensatory vasodilation during autoregulation and volume-flow relationships during hypoperfusion.

Nonlinear Susceptibilities in a Three-Level Atomic System

We have studied the effect of the propagation of two strong fields of different frequencies on the nonlinear susceptibility in a medium composed of identical stationary three-level atoms in V-configuration. In particular, we show that each field influences the steady-state susceptibility, absorption and refractive-index change experienced by the other field. At large field strengths of one field, the second field experiences less absorption and an enhanced refractive index change.

Influence of coronary flow and pressure on cardiac function and coronary vascular volume.

Influence of coronary flow and pressure on cardiac function and coronary vascular volume.