Assessment of Myocardial Function During Blood Pressure Manipulations Using Feature Tracking Cardiovascular Magnetic Resonance.

Background: Coronary autoregulation is a feedback system, which maintains near-constant myocardial blood flow over a range of mean arterial pressure (MAP). Yet in emergency or peri-operative situations, hypotensive or hypertensive episodes may quickly arise. It is not yet established how rapid blood pressure changes outside of the autoregulation zone (ARZ) impact left (LV) and right ventricular (RV) function. Using cardiovascular magnetic resonance (CMR) imaging, measurements of myocardial tissue oxygenation and ventricular systolic and diastolic function can comprehensively assess the heart throughout a range of changing blood pressures. Design and methods: In 10 anesthetized swine, MAP was varied in steps of 10-15 mmHg from 29 to 196 mmHg using phenylephrine and urapidil inside a 3-Tesla MRI scanner. At each MAP level, oxygenation-sensitive (OS) cine images along with arterial and coronary sinus blood gas samples were obtained and blood flow was measured from a surgically implanted flow probe on the left anterior descending coronary artery. Using CMR feature tracking-software, LV and RV circumferential systolic and diastolic strain parameters were measured from the myocardial oxygenation cines. Results: LV and RV peak strain are compromised both below the lower limit (LV: Δ1.2 ± 0.4%, RV: Δ4.4 ± 1.2%, p < 0.001) and above the upper limit (LV: Δ2.1 ± 0.4, RV: Δ5.4 ± 1.4, p < 0.001) of the ARZ in comparison to a baseline of 70 mmHg. LV strain demonstrates a non-linear relationship with invasive and non-invasive measures of oxygenation. Specifically for the LV at hypotensive levels below the ARZ, systolic dysfunction is related to myocardial deoxygenation (ß = -0.216, p = 0.036) in OS-CMR and both systolic and diastolic dysfunction are linked to reduced coronary blood flow (peak strain: ß = -0.028, p = 0.047, early diastolic strain rate: ß = 0.026, p = 0.002). These relationships were not observed at hypertensive levels. Conclusion: In an animal model, biventricular function is compromised outside the coronary autoregulatory zone. Dysfunction at pressures below the lower limit is likely caused by insufficient blood flow and tissue deoxygenation. Conversely, hypertension-induced systolic and diastolic dysfunction points to high afterload as a cause. These findings from an experimental model are translatable to the clinical peri-operative environment in which myocardial deformation may have the potential to guide blood pressure management, in particular at varying individual autoregulation thresholds.

Relationship between myocardial oxygenation and blood pressure: Experimental validation using oxygenation-sensitive cardiovascular magnetic resonance.

BACKGROUND: The relationship between mean arterial pressure (MAP) and coronary blood flow is well described. There is autoregulation within a MAP range of 60 to 140 mmHg providing near constant coronary blood flow. Outside these limits flow becomes pressure-dependent. So far, response of myocardial oxygenation to changes in pressure and flow has been more difficult to assess. While established techniques mostly require invasive approaches, Oxygenation-Sensitive (OS) Cardiovascular Magnetic Resonance (CMR) is a technique that can non-invasively assess changes in myocardial tissue oxygenation. The purpose of this study was to follow myocardial oxygenation over a wide range of blood pressure variation within and outside known coronary autoregulatory limits using OS-CMR, and to relate these data to coronary hemodynamics. METHODS: Ten anaesthetized swine (German Large White) underwent left-sided thoracotomy and attachment of a perivascular flow probe to the proximal left anterior descending (LAD) coronary artery for continuous measurement of blood flow (QLAD). Thereafter, animals were transferred into a 3T MRI scanner. Mean arterial pressure (MAP) was varied in 10-15 mmHg steps by administering alpha1-receptor agents phenylephrine or urapidil. For each MAP level, OS-CMR images as well as arterial and coronary sinus blood gas samples were obtained simultaneously during brief periods of apnea. Relative changes (Δ) of coronary sinus oxygen saturation (ScsO2), oxygen delivery (DO2) and demand (MVO2), extraction ratio (O2ER) and excess (Ω) from respective reference levels at a MAP of 70 mmHg were determined and were compared to %change in OS-signal intensity (OS-SI) in simultaneously acquired OS-CMR images. RESULTS: QLAD response indicated autoregulation between MAP levels of 52 mmHg (lower limit) and127 mmHg (upper limit). OS-CMR revealed a global myocardial oxygenation deficit occurring below the lower autoregulation limit, with the nadir of OS-SI at -9.0%. With MAP values surpassing 70 mmHg, relative OS-SI increased to a maximum of +10.6%. Consistent with this, ΔScsO2, ΔDO2, ΔMVO2, ΔO2ER and ΔΩ responses indicated increasing mismatch of oxygenation balance outside the autoregulated zone. Changes in global OS-CMR were significantly correlated with all of these parameters (p≤0.02) except with ΔMVO2. CONCLUSION: OS-CMR offers a novel and non-invasive route to evaluate the effects of blood pressure variations, as well as of cardiovascular drugs and interventions, on global and regional myocardial oxygenation, as demonstrated in a porcine model. OS-CMR identified mismatch of O2 supply and demand below the lower limit of coronary autoregulation. Vasopressor induced acute hypertension did not compromise myocardial oxygenation in healthy hearts despite increased cardiac workload and O2 demand. The clinical usefulness of OS-CMR remains to be established.

The vibrational dynamics of 3D HOCl above dissociation.

We explore the classical vibrational dynamics of the HOCl molecule for energies above the dissociation energy of the molecule. Above dissociation, we find that the classical dynamics is dominated by an invariant manifold which appears to stabilize two periodic orbits at energies significantly above the dissociation energy. These stable periodic orbits can hold a large number of quantum states and likely can support a significant quasibound state of the molecule, well above the dissociation energy. The classical dynamics and the lifetime of quantum states on the invariant manifold are determined.

Asymptotic observability of low-dimensional powder chaos in a three-degrees-of-freedom scattering system.

We treat a chaotic Hamiltonian scattering system with three degrees of freedom where the chaotic invariant set is of low dimension. Then the chaos and its structure are not visible in scattering functions plotted along one-dimensional lines in the set of asymptotic initial conditions. We show that an asymptotic observer can nevertheless see the structure of the chaotic set in an appropriate scattering function on the two-dimensional impact parameter plane and in the doubly differential cross section. Rainbow singularities in the cross section carry over the symbolic dynamics of the chaotic set into the cross section. A smooth image of the fractal structure of the chaotic set can be reconstructed on the domain of the cross section.

Fractal scattering dynamics of the three-dimensional HOCl molecule.

We compare the 2D and 3D classical fractal scattering dynamics of Cl and HO for energies just above dissociation of the HOCl molecule, using a realistic potential energy surface for the HOCl molecule and techniques developed to analyze 3D chaotic scattering processes. For parameter regimes where the HO dimer initially has small vibrational energy, only small intervals of initial conditions show fractal scattering behavior and the scattering process is well described by a 2D model. For parameter regimes where the HO dimer initially has large vibrational energy, the scattering process is fully 3D and is dominated by fractal behavior.

The Fock space method of vibrational analysis.

A reformulation of a semiclassical theory that presently seems uniquely capable of interpreting generic complex multiresonant vibrational spectra is presented. Once given the spectroscopic Hamiltonian which reveals the set of possible resonant couplings and its eigenstates, the new and old formulations both yield without any further computation level by level dynamical assignments for the spectra. Computing a simple trajectory in phase space reveals the motions that when quantized yield the assigned levels. The reformulation introduces two new projected representations of the wave functions. The first is in action space and the second in angle space. The projected representations often allow the reduced angle space, where nodal searches are made, to be of lower dimension than formally occurred. In addition the action representation is a similarly lower dimension lattice representation whose discreteness and regularity allow higher reduced dimensions to be studied. The lattice representation is used to produce a significantly more complete and detailed assignment of the thiophosgene spectrum than previously published.

Demixing and cleaning of wave functions by projection, application to the assignment of molecular vibrations.

It is shown how the projection of a quantum mechanical state into an appropriate subspace of the Hilbert space can be useful for the classification and the assignment of states. The projection cleans the wave function and decomposes mixtures caused by near-accidental degeneracy. The idea is applied to vibrational states of the molecule CF(3)CHFI obtained from an algebraic Hamiltonian.

Chaotic scattering in a molecular system.

We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincaré surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.

Assignment and extracting dynamics from experimentally and theoretically obtained spectroscopic hamiltonians in the complex spectral and classically chaotic regions.

An analysis of existing algebraic multiresonance spectroscopic Hamiltonians, derived by fitting to experimental data or from classical canonical or quantum Van Vleck perturbation theory, allows without any significant further classical or quantum calculation the assignment of quantum numbers and motions to states observed in spectra that were previously thought to be irregular or just unassignable. In such cases, inspection of the amplitude and phase of eigenfunctions previously calculated in the Hamiltonians derivation process but now transformed to a reduced dimension semiclassical action-angle representation reveals extremely simple albeit unfamiliar topologies that give quantum numbers by simply counting nodes and phase advances. The topology allows these simple wave functions to be sorted into dynamically different excitation ladders or classes of states which are associated with different regions of phase space. The rungs of these ladders or the states in the classes intersperse in energy causing the spectral complexity. No experimental procedure allows such sorting. The success of the work stems from (1) the qualitative insights of nonlinear dynamics, (2) the conversion of the quantum problem in full dimension to a semiclassical one in reduced dimension by use of a canonical transform that takes advantage of the polyad and other constants of the motion, and (3) the judicious choice of the reduced angle variables to reflect rational ratio resonance frequency conditions. This leads to localization of those semiclassical wave functions, which are affected by the particular resonance. In reverse, the localized appearance of the reduced dimension wave function reveals which resonances govern it and makes sorting visually simple. The success of the work also stems from (4) the revealing use of plots of phase advances as well as the usual densities of the eigenstates for sorting and assignment purposes. Even in classically chaotic regions, organizing trajectories, which correspond to averages over regional phase space structures that need not be computed, can easily be drawn as the structure about which eigenfunction localization takes place. The organizing trajectories when transformed back to the full dimensional configuration space reveal the internal molecular motions. The complexity of the usual quantum stationary and propagated wave functions and associated classical trajectories forbids most often such assignments and sorting. This procedure brings the ability to interpret complex vibrational spectra to a degree previously thought possible only for lower excitations. The new methodology replaces and extends the computationally more difficult parts of a procedure used by the authors that was applied successfully to several molecules during the past few years. The new methodology is applied to DCO, CHBrClF, and the bending of acetylene.

Dynamics of radiation induced isomerization for HCN-CNH.

We have analyzed the dynamics underlying the use of sequential radiation pulses to control the isomerization between the HCN and the CNH molecules. The appearance of avoided crossings among Floquet eigenphases as the molecule interacts with the radiation pulses is the key to understanding the isomerization dynamics, both in the adiabatic and nonadiabatic regimes. We find that small detunings of the incident pulses can have a significant effect on the outcome of the isomerization process for the model we consider.

Assignment and extraction of dynamics of a small molecule with a complex vibrational spectrum: thiophosgene.

The dispersed fluorescence spectrum of the ground electronic state of thiophosgene, SCCl2, is analyzed in a very complex region of vibrational excitation, 7000-9000 cm(-1). The final result is that most of the inferred excited vibrational levels are assigned in terms of approximate constants of the motion. Furthermore, each level is associated with a rung on a ladder of quantum states on the basis of common reduced dimension fundamental motions. The resulting ladders cannot be identified by any experimental means, and it is the interspersing in energy of their rungs that makes the spectrum complex even after the process of level separation into polyads. Van Vleck perturbation theory is used to create polyad constants of the motion and a spectroscopic Hamiltonian from a potential fitted to experimental data. The eigen functions of this spectroscopic Hamiltonian are rewritten as semiclassical wave functions and transformed to a representation that allows us to analyze and assign the spectra with no other work other than to utilize concepts from nonlinear dynamics.