Stochastic Trajectories Research Articles

Calculating nonlinear response functions for multidimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion.

We present a methodology for simulating multidimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.

A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics

The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models, especially the car-following (CF) models. These models of the movement of vehicles serve as the backbone of traffic flow analysis, simulation, autonomous vehicle development, etc. Two-dimensional (2D) vehicular movement is basically stochastic and is the result of interactions between a driver’s behavior and a vehicle’s characteristics. Current microscopic models either neglect 2D noise, or overlook vehicle dynamics. The modeling capabilities, thus, are limited, so that stochastic lateral movement cannot be reproduced. The present research extends an intelligent driver model (IDM) by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model, with vehicle dynamics based on the stochastic differential equation (SDE) theory. Control inputs from the vehicle include the steer rate and longitudinal acceleration, both of which are developed based on an idea from a traditional intelligent driver model. The stochastic stability condition is analyzed on the basis of Lyapunov theory. Numerical analysis is used to assess the two cases: (i) when a vehicle accelerates from a standstill and (ii) when a platoon of vehicles follow a leader with a stop-and-go speed profile, the formation of congestion and subsequent dispersion are simulated. The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement. The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.

Online inference of lane changing events for connected and automated vehicle applications with analytical logistic diffusion stochastic differential equation

Inferences of the lane changing behaviors (including lane changing initiation moment LCIM, cross-lane-mark moment CLMM, and lane changing duration LCD) of the surrounding vehicles and taking actions to avoid collision are essential for the safe operation of connected and autonomous vehicles (CAVs). The majority of current models rely on data-driven methods that need to be trained before deployment. Besides, an analytical and stochastic formulation of the lateral model which can generate CLMM and LCD distribution and adjust the parameters online is still lacking. To the best of our knowledge, currently, no method can provide an analytically stochastic lateral movement that explicitly considers the system noise and simultaneously outputs the information of lane changing initiation moment, cross-lane-mark moment, and lane changing duration in a real-time manner. To fill such a gap, a stochastic lateral trajectory framework with parsimonious parameters is established and an online simultaneous inference of LCIM, CLMM, and LCD is developed. The proposed method is tested with the highD and NGSIM datasets. The results show that 1) computational efficiency-wise, the algorithm takes milliseconds to run, which suggests promising prospects for field deployment; 2) the false negative and false positive errors of the LCIM inference are as low as 1.5%, indicating that the method is robust to the stochastic noise; 3) LCIM inference is insensitive to the lane width, which means the model is error tolerant when such information is lacking; and 4) the error of CLMM inference is within 2 sec, while most of the error of LCD locates within 4 sec, suggesting satisfactory performance.

A new symmetry for large deviation functions of time-integrated dynamical variables

A new type of symmetry in the large deviation function of a time-integrated current is introduced. This current is different from the fluctuating entropy production for which the large deviation function is symmetric in the content of the fluctuation theorem. The origin of this symmetry, similar to that of the Gallavotti-Cohen-Evans-Morriss symmetry, is related to time-reversal. The symmetry is more unveiled when one performs an appropriate grouping of stochastic trajectories in the space of microscopic configurations. It turns out that the characteristic polynomial of the modified generator of this current is not symmetric; however, its minimum eigenvalue is symmetric.

Construction of special soliton solutions to the stochastic Riccati equation

Abstract A scheme for the analytical stochastization of ordinary differential equations (ODEs) is presented in this article. Using Itô calculus, an ODE is transformed into a stochastic differential equation (SDE) in such a way that the analytical solutions of the obtained equation can be constructed. Furthermore, the constructed stochastic trajectories remain bounded in the same interval as the deterministic solutions. The proposed approach is in a stark contrast to methods based on the randomization of solution trajectories and is not focused on the analysis of martingales. This article extends the theory of Itô calculus by directly implementing it into analytical schemes for the solution of differential equations based on the generalized operator of differentiation. The efficacy of the presented analytical stochastization techniques is demonstrated by deriving stochastic soliton solutions to the Riccati differential equation. The presented semi-analytical stochastization scheme is relevant for the investigation of the global dynamics of different biological and biomedical processes where the variation interval of the stochastic solution is predetermined by the rationale of the model.

Convex Approach to Covariance Control with Application to Stochastic Low-Thrust Trajectory Optimization

This paper outlines a novel approach to the design of optimal space trajectories under significant uncertainty. Finite-horizon covariance control, i.e., the steering of a system from an initial probability distribution to a desired one at a prescribed time, is employed to plan an optimal nominal path along with a robust feedback controller that compensates for exogenous in-flight disturbances. A mindful convexification strategy is devised to recast the nonlinear covariance control problem as a deterministic convex optimization problem. The convexification is based on a convenient change of variables that allows for relaxing the covariance matrix discrete-time propagation into a set of semidefinite cone constraints. While featuring a larger feasible space, the relaxed problem shares the same optimal solution as the original one. The lossless property of the relaxation is analytically proven by leveraging optimal control theory and discussed on the basis of numerical experiments. Monte Carlo campaigns are carried out to validate the in-flight performance of the attained control policies.

Monitoring-induced entanglement entropy and sampling complexity

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

Nucleation causes an actin network to fragment into multiple high-density domains

Actin networks rely on nucleation mechanisms to generate new filaments because spontaneous nucleation is kinetically disfavored. Branching nucleation of actin filaments by actin-related protein (Arp2/3), in particular, is critical for actin self-organization. In this study, we use the simulation platform for active matter MEDYAN to generate 2000 s long stochastic trajectories of actin networks, under varying Arp2/3 concentrations, in reaction volumes of biologically meaningful size (>20 μm3). We find that the dynamics of Arp2/3 increase the abundance of short filaments and increases network treadmilling rate. By analyzing the density fields of F-actin, we find that at low Arp2/3 concentrations, F-actin is organized into a single connected and contractile domain, while at elevated Arp2/3 levels (10 nM and above), such high-density actin domains fragment into smaller domains spanning a wide range of volumes. These fragmented domains are extremely dynamic, continuously merging and splitting, owing to the high treadmilling rate of the underlying actin network. Treating the domain dynamics as a drift-diffusion process, we find that the fragmented state is stochastically favored, and the network state slowly drifts toward the fragmented state with considerable diffusion (variability) in the number of domains. We suggest that tuning the Arp2/3 concentration enables cells to transition from a globally coherent cytoskeleton, whose response involves the entire cytoplasmic network, to a fragmented cytoskeleton, where domains can respond independently to locally varying signals.

Markov trajectories: Microcanonical Ensembles based on empirical observables as compared to Canonical Ensembles based on Markov generators

The Ensemble of trajectories $x(0 \leq t \leq T)$ produced by the Markov generator $M$ can be considered as 'Canonical' for the following reasons : (C1) the probability of the trajectory $x(0 \leq t \leq T)$ can be rewritten as the exponential of a linear combination of its relevant empirical time-averaged observables $E_n$, where the coefficients involving the Markov generator are their fixed conjugate parameters; (C2) the large deviations properties of these empirical observables $E_n$ for large $T$ are governed by the explicit rate function $I^{[2.5]}_M (E_.) $ at Level 2.5, while in the thermodynamic limit $T=+\infty$, they concentrate on their typical values $E_n^{typ[M]}$ determined by the Markov generator $M$. This concentration property in the thermodynamic limit $T=+\infty$ suggests to introduce the notion of the 'Microcanonical Ensemble' at Level 2.5 for stochastic trajectories $x(0 \leq t \leq T)$, where all the relevant empirical variables $E_n$ are fixed to some values $E^*_n$ and cannot fluctuate anymore for finite $T$. The goal of the present paper is to discuss its main properties : (MC1) when the long trajectory $x(0 \leq t \leq T) $ belongs the Microcanonical Ensemble with the fixed empirical observables $E_n^*$, the statistics of its subtrajectory $x(0 \leq t \leq \tau) $ for $1 \ll \tau \ll T $ is governed by the Canonical Ensemble associated to the Markov generator $M^*$ that would make the empirical observables $E_n^*$ typical ; (MC2) in the Microcanonical Ensemble, the central role is played by the number $\Omega^{[2.5]}_T(E^*_.) $ of stochastic trajectories of duration $T$ with the given empirical observables $E^*_n$, and by the corresponding explicit Boltzmann entropy $S^{[2.5]}( E^*_. ) = [\ln \Omega^{[2.5]}_T(E^*_.)]/T $. This general framework is applied to continuous-time Markov Jump processes and to discrete-time Markov chains with illustrative examples.

Conditioning diffusion processes with killing rates

When the unconditioned process is a diffusion submitted to a space-dependent killing rate , various conditioning constraints can be imposed for a finite time horizon T. We first analyze the conditioned process when one imposes both the surviving distribution at time T and the killing-distribution for the intermediate times t ∈ [0, T]. When the conditioning constraints are less-detailed than these full distributions, we construct the appropriate conditioned processes via the optimization of the dynamical large deviations at level 2.5 in the presence of the conditioning constraints that one wishes to impose. Finally, we describe various conditioned processes for the infinite horizon T → +∞. This general construction is then applied to two illustrative examples in order to generate stochastic trajectories satisfying various types of conditioning constraints: the first example concerns the pure diffusion in dimension d with the quadratic killing rate , while the second example is the Brownian motion with uniform drift submitted to the delta killing rate k(x) = kδ(x) localized at the origin x = 0.

Coronary sinus electrogram characteristics predict termination of AF with ablation and long-term clinical outcome.

Markers predicting atrial fibrillation (AF) termination and freedom from AF/atrial tachycardia (AT) has been proposed. This study aimed to evaluate the role of novel coronary sinus (CS) electrogram characteristics in predicting the acute ablation response and freedom from AF/AT during follow-up. Patients undergoing ablation for persistent AF as part of the Stochastic Trajectory Analysis of Ranked signals mapping study were included. Novel CS electrogram characteristics including CS cycle length variability (CLV) and CS activation pattern stability (APS) and proportion of low voltage zones (LVZs) were reviewed as potential predictors for AF termination on ablation and freedom from AF/AT during follow-up. The relationship between localized driver characteristics and CS electrogram characteristics was also assessed. Sixty-five patients were included. AF termination was achieved in 51 patients and 80% of patients were free from AF/AT during a follow-up of 29.5 ± 3.7 months. CS CLV of <30 ms, CS APS of ≥30% and proportion of LVZ < 30% showed high diagnostic accuracy in predicting AF termination on ablation and freedom from AF/AT during follow-up (CS CLV odds ratio [OR] 25.6, area under the curve [AUC] 0.91; CS APS OR 15.9, AUC 0.94; proportion of LVZs OR 21.4, AUC 0.88). These markers were independent predictors of AF termination on ablation and AF/AT recurrence during follow-up. Ablation of a smaller number of drivers that demonstrate greater dominance strongly correlate with greater CS organization. Novel CS electrogram characteristics were independent predictors of AF termination and AF/AT recurrence during follow-up. These markers can potentially aid in predicting outcomes and guide ablation and follow-up strategies.

Conditioning two diffusion processes with respect to their first-encounter properties

We consider two independent identical diffusion processes that annihilate upon meeting in order to study their conditioning with respect to their first-encounter properties. For the case of finite horizon T < +∞, the maximum conditioning consists in imposing the probability P*(x, y, T) that the two particles are surviving at positions x and y at time T, as well as the probability γ*(z, t) of annihilation at position z at the intermediate times t ∈ [0, T]. The adaptation to various conditioning constraints that are less-detailed than these full distributions is analyzed via the optimization of the appropriate relative entropy with respect to the unconditioned processes. For the case of infinite horizon T = +∞, the maximum conditioning consists in imposing the first-encounter probability γ*(z, t) at position z at all finite times , whose normalization [1 − S*(∞)] determines the conditioned probability S*(∞) ∈ [0, 1] of forever-survival. This general framework is then applied to the explicit cases where the unconditioned processes are respectively two Brownian motions, two Ornstein–Uhlenbeck processes, or two tanh-drift processes, in order to generate stochastic trajectories satisfying various types of conditioning constraints. Finally, the link with the stochastic control theory is described via the optimization of the dynamical large deviations at level 2.5 in the presence of the conditioning constraints that one wishes to impose.

Stochastic control of ecological networks.

The paper models the maintenance of ecological networks in forest environments, built from bioreserves, patches and corridors, when these grids are subject to random processes such as extreme natural events. It also outlines a management plan to support the optimized results. After presenting the random graph-theoretic framework, we apply the stochastic optimal control to the graph dynamics. Our results show that the preservation of the network architecture cannot be achieved, under stochastic control, over the entire duration. It can only be accomplished, at the cost of sacrificing the links between the patches, by increasing the usage of the control devices. This would have a negative effect on the species migration by causing congestion among the channels left at their disposal. The optimal scenario, in which the shadow price is at its lowest and all connections are well-preserved, occurs at half of the course, be it the only optimal stopping moment found on the stochastic optimal trajectories. In such a scenario, the optimal forestry management policy has to integrate agility, integrated response, and quicker response time.

Sampling rare trajectories using stochastic bridges.

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

Perfusion Maps Acquired From Dynamic Angiography MRI Using Deep Learning Approaches.

A typical stroke MRI protocol includes perfusion-weighted imaging (PWI) and MR angiography (MRA), requiring a second dose of contrast agent. A deep learning method to acquire both PWI and MRA with single dose can resolve this issue. To acquire both PWI and MRA simultaneously using deep learning approaches. Retrospective. A total of 60 patients (30-73 years old, 31 females) with ischemic symptoms due to occlusion or ≥50% stenosis (measured relative to proximal artery diameter) of the internal carotid artery, middle cerebral artery, or anterior cerebral artery. The 51/1/8 patient data were used as training/validation/test. A 3 T, time-resolved angiography with stochastic trajectory (contrast-enhanced MRA) and echo planar imaging (dynamic susceptibility contrast MRI, DSC-MRI). We investigated eight different U-Net architectures with different encoder/decoder sizes and with/without an adversarial network to generate perfusion maps from contrast-enhanced MRA. Relative cerebral blood volume (rCBV), relative cerebral blood flow (rCBF), mean transit time (MTT), and time-to-max (Tmax ) were mapped from DSC-MRI and used as ground truth to train the networks and to generate the perfusion maps from the contrast-enhanced MRA input. Normalized root mean square error, structural similarity (SSIM), peak signal-to-noise ratio (pSNR), DICE, and FID scores were calculated between the perfusion maps from DSC-MRI and contrast-enhanced MRA. One-tailed t-test was performed to check the significance of the improvements between networks. P values < 0.05 were considered significant. The four perfusion maps were successfully extracted using the deep learning networks. U-net with multiple decoders and enhanced encoders showed the best performance (pSNR 24.7 ± 3.2 and SSIM 0.89 ± 0.08 for rCBV). DICE score in hypo-perfused area showed strong agreement between the generated perfusion maps and the ground truth (highest DICE: 0.95 ± 0.04). With the proposed approach, dynamic angiography MRI may provide vessel architecture and perfusion-relevant parameters simultaneously from a single scan. 3 TECHNICAL EFFICACY: Stage 5.

Dynamic Interrogation of Stochastic Transcriptome Trajectories Using Disease Associated Genes Reveals Distinct Origins of Neurological and Psychiatric Disorders.

The advent of open access to genomic data offers new opportunities to revisit old clinical debates while approaching them from a different angle. We examine anew the question of whether psychiatric and neurological disorders are different from each other by assessing the pool of genes associated with disorders that are understood as psychiatric or as neurological. We do so in the context of transcriptome data tracked as human embryonic stem cells differentiate and become neurons. Building upon probabilistic layers of increasing complexity, we describe the dynamics and stochastic trajectories of the full transcriptome and the embedded genes associated with psychiatric and/or neurological disorders. From marginal distributions of a gene’s expression across hundreds of cells, to joint interactions taken globally to determine degree of pairwise dependency, to networks derived from probabilistic graphs along maximal spanning trees, we have discovered two fundamentally different classes of genes underlying these disorders and differentiating them. One class of genes boasts higher variability in expression and lower dependencies (High Expression Variability-HEV genes); the other has lower variability and higher dependencies (Low Expression Variability-LEV genes). They give rise to different network architectures and different transitional states. HEV genes have large hubs and a fragile topology, whereas LEV genes show more distributed code during the maturation toward neuronal state. LEV genes boost differentiation between psychiatric and neurological disorders also at the level of tissue across the brain, spinal cord, and glands. These genes, with their low variability and asynchronous ON/OFF states that have been treated as gross data and excluded from traditional analyses, are helping us settle this old argument at more than one level of inquiry.

Determination of Contrast Timing by Time-Resolved Magnetic Resonance Angiography in Patients With Bidirectional Glenn and Hemi-Fontan Anastomoses.

Children with single-ventricle congenital heart disease undergo a series of operations to maintain their pulmonary circulation including bidirectional Glenn (BDG) or hemi-Fontan in the second stage to create a superior cavopulmonary anastomosis. We aimed to optimize cardiovascular angiography protocols by determining optimal contrast timing of pulmonary and systemic circulation on magnetic resonance angiography (MRA) performed with the technique of time-resolved imaging with interleaved stochastic trajectories (TWIST). Cardiac TWIST MRA with lower extremity (LE) contrast injection was analyzed in 92 consecutive patients with a BDG or hemi-Fontan anastomosis. Contrast arrival time to inferior vena cava was set to zero to determine the relative time-to-peak (TTP) of the target vessels. Time-to-peak of each vessel was compared by age (<2 or ≥2 y), ejection fraction (<54% or ≥54%), the median values of heart rate (<111 or ≥111 beats per minute), body surface area (BSA, <0.59 or ≥0.59), cardiac index (<6.04 or ≥6.04), and indexed ascending aorta flow (AscAo_i, <5.3 or ≥5.3). The TTP of the vessels was also correlated with the volumetric parameters. The mean age of 92 patients (32 female, 60 male) was 3.1 years (0.7-5.6 years). With LE injection, the first peak was depicted in AscAo. Time-to-peak of the pulmonary arteries was approximately 9 seconds later than AscAo. The TTP difference between pulmonary arteries and AscAo was shorter in high heart rate group (8.3 vs 10 seconds, P < 0.001). The TTP difference between AscAo and the mean of pulmonary arteries was significantly shorter in high cardiac index group (8.4 vs 9.9 seconds, P < 0.01) and high AscAo_i group (8.7 vs 9.7 seconds, P = 0.03). The TTP differences were not significant by age, ejection fraction, and BSA. Cardiac index and AscAo_i were negatively correlated with all TTPs except AscAo. The ejection fraction, stroke volume, and atrioventricular regurgitation fraction did not correlate with the TTP. In patients with BDG or hemi-Fontan anastomosis, TTP of the pulmonary arteries on TWIST MRA via LE intravenous injection is approximately 9 seconds later than AscAo, approximately 8 and 10 seconds later in high and low heart rate groups, respectively. Cardiac index and AscAo_i have less effect on the TTP than the heart rate. There was no TTP difference of the pulmonary arteries by age, BSA, and ejection fraction and no correlation with ejection fraction, stroke volume, and atrioventricular regurgitation fraction. These data can be used to guide timing of pulmonary arterial enhancement of single-ventricle patients after BDG or hemi-Fontan anastomosis.

Quantum coherence protection by noise

In this paper, we propose a scheme to protect quantum coherence by adding another noise. We consider an example of a Jaynes–Cummings model coupled to an external non-Markovian bosonic bath. We solve this model by using the dressed state method in the presence of a stochastic coupling and obtain the density matrix by numerically averaging many stochastic trajectories. We show that the noisy atom-cavity coupling can effectively suppress both the relaxation and dephasing effects caused by the leakage of the cavity. Besides, we further illustrate the impacts of the standard deviation of the noisy coupling and the non-Markovian memory effect on the coherence protection. Then, the mechanism of the protection is analyzed. It is our hope that our research may open a new path to consider the role of noise in quantum coherence preservation.

Effective entropy production and thermodynamic uncertainty relation of active Brownian particles

Understanding stochastic thermodynamics of the active Brownian particles system has been an important topic in very recent years. However, thermodynamic uncertainty relation (TUR), a general inequality describing how the precision of an arbitrary observable current is constraint by energy dissipation, has not been fully studied for a many-body level. Here, we address such an issue in a general model of an active Brownian particles system by introducing an effective Fokker–Planck equation, which allows us to identify a generalized entropy production only by tracking the stochastic trajectory of particles' position, wherein an activity and configuration dependent diffusion coefficient come into play an important role. Within this framework, we are able to analyze the entropic bound as well as TUR associated with any generalized currents in the systems. Furthermore, the effective entropy production has been found to be a reliable measure to quantify the dynamical irreversibility, capturing the interface and defects of motility induced phase separation. We expect the new conceptual quantities proposed here to be broadly used in the context of active matter.

Effect of Contrast Agent Dose Reduction on Vascular Enhancement and Image Quality in Thoracoabdominal Dynamic 3-Dimensional Magnetic Resonance Angiography: A Systematic Intraindividual Analysis in Pigs.

High spatial and temporal resolution contrast-enhanced magnetic resonance angiography (MRA) with gadolinium-based contrast agents (GBCAs) at standard dose offers both detailed anatomic information on both arterial and venous vessels and hemodynamic characteristics. Several preclinical and clinical dynamic 3-dimensional (3D) MRA studies that focused on arterial vessels only proposed that high image quality may also be achieved with significantly reduced GBCA doses, calling into question the need to use standard doses. A systematic analysis of GBCA doses and resulting image quality for both arteries and veins has not yet been performed. The purpose of this study was therefore to systematically analyze dose-dependent vascular enhancements in dynamic 3D-MRA of the thoracoabdominal vasculature at 1.5 T in an animal model to determine the optimal contrast agent protocol for optimized vascular assessment. The vascular enhancement in thoracoabdominal dynamic 3D-MRA (time-resolved angiography with interleaved stochastic trajectories, TWIST at 1.5 T) was interindividually and intraindividually compared in 5 anesthetized Göttingen minipigs using gadobutrol at the standard dose (0.1 mmol/kg body weight, ie, 0.1 mL/kg) and at reduced doses (0.08, 0.06, 0.04, 0.02 mmol/kg) in a randomized order. All injections were performed at 2 mL/s followed by 20 mL saline. Images were quantitatively analyzed, measuring signal intensities in 5 regions that covered the passage of the GBCA through the body at different representative stages of circulation (pulmonary, arterial, and venous system). The evaluation of GBCA dose-dependent signal intensity changes in the different vascular regions was performed by linear regression analysis.The qualitative image analysis of dynamic 3D-MRA by 3 independent radiologists included the visibility of 25 arterial and venous vessel segments at different stages of GBCA passage. Possible quality losses were statistically tested by comparing image quality ratings at the reduced dose with that of the standard dose using Friedman test followed by Dunn post hoc test for multiple comparison. Significance was stated at P < 0.05. Quantitative analysis revealed shorter time-to-peak intervals and bolus durations in line with decreasing GBCA dose and volume in all vessels. Although the peak signal was almost independent of the administered GBCA dose at the level of the pulmonary trunk, a linear signal decrease in the abdominal aorta ( r2 = 0.96), the renal arteries ( r2 = 0.99), the inferior vena cava ( r2 = 0.99), and the portal vein ( r2 = 0.97) was observed. Cumulative analysis of arterial segments revealed significantly lower image quality at doses below 40% of the standard dose, whereas in venous segments, significantly lower image quality was observed at doses below 60% of the standard dose. In dynamic 3D-MRA at 1.5 T, dose reduction leads to a signal loss that is most pronounced in the venous system and results in significantly lower image quality according to the dose and vessels of interest. Careful dose reduction is thus required according to the specific diagnostic needs. For dynamic 3D-MRA of the arterial and venous system, GBCA doses of at least 60% of the standard dose up to the full dose are preferable, whereas 40% of the standard dose seems feasible if only the arterial system is to be imaged.