Jussi Schultz

Endothelial wall shear stress (ESS) is a biomechanical force which plays a role in the formation and evolution of atherosclerotic lesions. The purpose of this study is to evaluate coronary computed tomography angiography (CCTA)-based ESS in coronary arteries without atherosclerosis, and to assess factors affecting ESS values. CCTA images from patients with suspected coronary artery disease were analyzed to identify coronary arteries without atherosclerosis. Minimal and maximal ESS values were calculated for 3-mm segments. Factors potentially affecting ESS values were examined, including sex, lumen diameter and distance from the ostium. Segments were categorized according to lumen diameter tertiles into small (< 2.6 mm), intermediate (2.6–3.2 mm) or large (≥ 3.2 mm) segments. A total of 349 normal vessels from 168 patients (mean age 59 ± 9 years, 39% men) were included. ESS was highest in the left anterior descending artery compared to the left circumflex artery and right coronary artery (minimal ESS 2.3 Pa vs. 1.9 Pa vs. 1.6 Pa, p < 0.001 and maximal ESS 3.7 Pa vs. 3.0 Pa vs. 2.5 Pa, p < 0.001). Men had lower ESS values than women, also after adjusting for lumen diameter (p < 0.001). ESS values were highest in small segments compared to intermediate or large segments (minimal ESS 3.8 Pa vs. 1.7 Pa vs. 1.2 Pa, p < 0.001 and maximal ESS 6.0 Pa vs. 2.6 Pa vs. 2.0 Pa, p < 0.001). A weak to strong correlation was found between ESS and distance from the ostium (ρ = 0.22–0.62, p < 0.001). CCTA-based ESS values increase rapidly and become widely scattered with decreasing lumen diameter. This needs to be taken into account when assessing the added value of ESS beyond lumen diameter in highly stenotic lesions.

Dual cardiac and respiratory gating is a well-known technique for motion compensation in nuclear medicine imaging. In this study, we present a new data fusion framework for dual cardiac and respiratory gating based on multidimensional microelectromechanical (MEMS) motion sensors. Our approach aims at robust estimation of the chest vibrations, that is, high-frequency precordial vibrations and low-frequency respiratory movements for prospective gating in positron emission tomography (PET), computed tomography (CT), and radiotherapy. Our sensing modality in the context of this paper is a single dual sensor unit, including accelerometer and gyroscope sensors to measure chest movements in three different orientations. Since accelerometer- and gyroscope-derived respiration signals represent the inclination of the chest, they are similar in morphology and have the same units. Therefore, we use principal component analysis (PCA) to combine them into a single signal. In contrast to this, the accelerometer- and gyroscope-derived cardiac signals correspond to the translational and rotational motions of the chest, and have different waveform characteristics and units. To combine these signals, we use independent component analysis (ICA) in order to obtain the underlying cardiac motion. From this cardiac motion signal, we obtain the systolic and diastolic phases of cardiac cycles by using an adaptive multi-scale peak detector and a short-time autocorrelation function. Three groups of subjects, including healthy controls (n = 7), healthy volunteers (n = 12), and patients with a history of coronary artery disease (n = 19) were studied to establish a quantitative framework for assessing the performance of the presented work in prospective imaging applications. The results of this investigation showed a fairly strong positive correlation (average r = 0.73 to 0.87) between the MEMS-derived (including corresponding PCA fusion) respiration curves and the reference optical camera and respiration belt sensors. Additionally, the mean time offset of MEMS-driven triggers from camera-driven triggers was 0.23 to 0.3 ± 0.15 to 0.17 s. For each cardiac cycle, the feature of the MEMS signals indicating a systolic time interval was identified, and its relation to the total cardiac cycle length was also reported. The findings of this study suggest that the combination of chest angular velocity and accelerations using ICA and PCA can help to develop a robust dual cardiac and respiratory gating solution using only MEMS sensors. Therefore, the methods presented in this paper should help improve predictions of the cardiac and respiratory quiescent phases, particularly with the clinical patients. This study lays the groundwork for future research into clinical PET/CT imaging based on dual inertial sensors.

We show that number and canonical phase (of a single mode optical field) are complementary observables. We also bound the measurement uncertainty region for their approximate joint measurements.

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance subgroups are possible. In particular, when the Hilbert space is 2ⁿ dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of 2ⁿ covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique in even prime-power dimensions.

We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy separately. We introduce the index of incompatibility as a quantifier of incompatibility in this multi-copy setting, as well as the notion of the compatibility stack representing various compatibility relations present in a given set of observables. We then prove a general structure theorem for multi-copy joint observables and use it to prove that all abstract compatibility stacks with three vertices have realizations in terms of quantum observables.