Rate control management of atrial fibrillation: may a mathematical model suggest an ideal heart rate?

BACKGROUND

Despite the routine prescription of rate control therapy for atrial fibrillation (AF), clinical evidence demonstrating a heart rate target is lacking. Aim of the present study was to run a mathematical model simulating AF episodes with a different heart rate (HR) to predict hemodynamic parameters for each situation.

METHODS

The lumped model, representing the pumping heart together with systemic and pulmonary circuits, was run to simulate AF with HR of 50, 70, 90, 110 and 130 bpm, respectively.

RESULTS

Left ventricular pressure increased by 57%, from 33.92±37.56 mmHg to 53.15±47.56 mmHg, and mean systemic arterial pressure increased by 27%, from 82.66±14.04 mmHg to 105.3±7.6 mmHg, at the 50 and 130 bpm simulations, respectively. Stroke volume (from 77.45±8.50 to 39.09±8.08 mL), ejection fraction (from 61.10±4.40 to 39.32±5.42%) and stroke work (SW, from 0.88±0.04 to 0.58±0.09 J) decreased by 50, 36 and 34%, at the 50 and 130 bpm simulations, respectively. In addition, oxygen consumption indexes (rate pressure product - RPP, tension time index per minute - TTI/min, and pressure volume area per minute - PVA/min) increased from the 50 to the 130 bpm simulation, respectively, by 186% (from 5598±1939 to 15995±3219 mmHg/min), 56% (from 2094±265 to 3257±301 mmHg s/min) and 102% (from 57.99±17.90 to 117.4±26.0 J/min). In fact, left ventricular efficiency (SW/PVA) decreased from 80.91±2.91% at 50 bpm to 66.43±3.72% at the 130 bpm HR simulation.

CONCLUSION

Awaiting compulsory direct clinical evidences, the present mathematical model suggests that lower HRs during permanent AF relates to improved hemodynamic parameters, cardiac efficiency, and lower oxygen consumption.

Compensatory Effect between Aortic Stiffening and Remodelling during Ageing

The arterial tree exhibits a complex spatio-temporal wave pattern, whose healthy behaviour depends on a subtle balance between mechanical and geometrical properties. Several clinical studies demonstrated that such a balance progressively breaks down during ageing, when the aorta stiffens and remodels by increasing its diameter. These two degenerative processes however, have different impacts on the arterial wave pattern. They both tend to compensate for each other, thus reducing the detrimental effect they would have had if they had arisen individually. This remarkable compensatory mechanism is investigated by a validated multi-scale model, with the aim to elucidate how aortic stiffening and remodelling quantitatively impact the complex interplay between forward and reflected backward waves in the arterial network. We focus on the aorta and on the pressure at the ventricular-aortic interface, which epidemiological studies demonstrate to play a key role in cardiovascular diseases.

Inter-species competition-facilitation in stochastic riparian vegetation dynamics

Riparian vegetation is a highly dynamic community that lives on river banks and which depends to a great extent on the fluvial hydrology. The stochasticity of the discharge and erosion/deposition processes in fact play a key role in determining the distribution of vegetation along a riparian transect. These abiotic processes interact with biotic competition/facilitation mechanisms, such as plant competition for light, water, and nutrients. In this work, we focus on the dynamics of plants characterized by three components: (1) stochastic forcing due to river discharges, (2) competition for resources, and (3) inter-species facilitation due to the interplay between vegetation and fluid dynamics processes. A minimalist stochastic bio-hydrological model is proposed for the dynamics of the biomass of two vegetation species: one species is assumed dominant and slow-growing, the other is subdominant, but fast-growing. The stochastic model is solved analytically and the probability density function of the plant biomasses is obtained as a function of both the hydrologic and biologic parameters. The impact of the competition/facilitation processes on the distribution of vegetation species along the riparian transect is investigated and remarkable effects are observed. Finally, a good qualitative agreement is found between the model results and field data.

Nonlinear and subharmonic stability analysis in film-driven morphological patterns

The interaction of a gravity-driven water film with an evolving solid substrate (calcite or ice) results in the formation of fascinating wavy patterns similar both in caves and in ice-falls. Due to their remarkable similarity, we adopt a unified approach in the study of pattern formation of longitudinally oriented organ-pipe-like structures, called flutings. Since the morphogenesis of cave patterns can evolve for millennia, they have an additional value as silent repositories of past climates. Fluting formation is studied with the aid of gradient expansion and center manifold projection. In particular, through gradient expansion, a Benney-type equation accounting for the movable boundary is obtained. The coupling with a wall evolution equation provides a morphodynamic model for fluting formation, explored through linear and nonlinear analyses. In this way, closed relationships for the selected wave number and for the finite amplitude are achieved. However, as finite-amplitude monochromatic waves may be destabilized by nonlinear interactions with other modes, we verify, through center manifold projection, the stability of the fundamental to subharmonic disturbances. Conclusively, we perform numerical simulations of the fully nonlinear equations to validate the theory results.

Thin-film-induced morphological instabilities over calcite surfaces

Precipitation of calcium carbonate from water films generates fascinating calcite morphologies that have attracted scientific interest over past centuries. Nowadays, speleothems are no longer known only for their beauty but they are also recognized to be precious records of past climatic conditions, and research aims to unveil and understand the mechanisms responsible for their morphological evolution. In this paper, we focus on crenulations, a widely observed ripple-like instability of the the calcite-water interface that develops orthogonally to the film flow. We expand a previous work providing new insights about the chemical and physical mechanisms that drive the formation of crenulations. In particular, we demonstrate the marginal role played by carbon dioxide transport in generating crenulation patterns, which are indeed induced by the hydrodynamic response of the free surface of the water film. Furthermore, we investigate the role of different environmental parameters, such as temperature, concentration of dissolved ions and wall slope. We also assess the convective/absolute nature of the crenulation instability. Finally, the possibility of using crenulation wavelength as a proxy of past flows is briefly discussed from a theoretical point of view.

Central Pressure Appraisal: Clinical Validation of a Subject-Specific Mathematical Model

Introduction

Current evidence suggests that aortic blood pressure has a superior prognostic value with respect to brachial pressure for cardiovascular events, but direct measurement is not feasible in daily clinical practice.

Aim

The aim of the present study is the clinical validation of a multiscale mathematical model for non-invasive appraisal of central blood pressure from subject-specific characteristics.

Methods

A total of 51 young male were selected for the present study. Aortic systolic and diastolic pressure were estimated with a mathematical model and were compared to the most-used non-invasive validated technique (SphygmoCor device, AtCor Medical, Australia). SphygmoCor was calibrated through diastolic and systolic brachial pressure obtained with a sphygmomanometer, while model inputs consist of brachial pressure, height, weight, age, left-ventricular end-systolic and end-diastolic volumes, and data from a pulse wave velocity study.

Results

Model-estimated systolic and diastolic central blood pressures resulted to be significantly related to SphygmoCor-assessed central systolic (r = 0.65 p <0.0001) and diastolic (r = 0.84 p<0.0001) blood pressures. The model showed a significant overestimation of systolic pressure (+7.8 (-2.2;14) mmHg, p = 0.0003) and a significant underestimation of diastolic values (-3.2(-7.5;1.6), p = 0.004), which imply a significant overestimation of central pulse pressure. Interestingly, model prediction errors mirror the mean errors reported in large meta-analysis characterizing the use of the SphygmoCor when non-invasive calibration is performed.

Conclusion

In conclusion, multi-scale mathematical model predictions result to be significantly related to SphygmoCor ones. Model-predicted systolic and diastolic aortic pressure resulted in difference of less than 10 mmHg in the 51% and 84% of the subjects, respectively, when compared with SphygmoCor-obtained pressures.

River bedform inception by flow unsteadiness: A modal and nonmodal analysis

River bedforms arise as a result of morphological instabilities of the stream-sediment interface. Dunes and antidunes constitute the most typical patterns, and their occurrence and dynamics are relevant for a number of engineering and environmental applications. Although flow variability is a typical feature of all rivers, the bedform-triggering morphological instabilities have generally been studied under the assumption of a constant flow rate. In order to partially address this shortcoming, we here discuss the influence of (periodic) flow unsteadiness on bedform inception. To this end, our recent one-dimensional validated model coupling Dressler's equations with a refined mechanistic sediment transport formulation is adopted, and both the asymptotic and transient dynamics are investigated by modal and nonmodal analyses.

An Integrated Methodology to Study Riparian Vegetation Dynamics: From Field Data to Impact Modeling

Riparian environments are highly dynamic ecosystems that support biodiversity and numerous services and that are conditioned by anthropogenic activities and climate change. In this work, we propose an integrated methodology that combines different research approaches-field studies and numerical and analytical modeling-in order to calibrate an ecohydrological stochastic model for riparian vegetation. The model yields vegetation biomass statistics and requires hydrological, topographical, and biological data as input. The biological parameters, namely, the carrying capacity and the flood-related decay rate, are the target of the calibration as they are related to intrinsic features of vegetation and site-specific environmental conditions. The calibration is here performed for two bars located within the riparian zone of the Cinca River (Spain). According to our results, the flood-related decay rate has a spatial dependence that reflects the zonation of different plant species over the study site. The carrying capacity depends on the depth of the phreatic surface, and it is adequately described by a right-skewed curve. The calibrated model well reproduces the actual biogeography of the Cinca riparian zone. The overall percentage absolute difference between the real and the computed biomass amounts to 9.3% and 3.3% for the two bars. The model is further used to predict the future evolution of riparian vegetation in a climate-change scenario. The results show that the change of hydrological regime forecast by future climate projections may induce dramatic reduction of vegetation biomass and strongly modify the Cinca riparian biogeography.

Hydrodynamic-driven stability analysis of morphological patterns on stalactites and implications for cave paleoflow reconstructions

A novel hydrodynamic-driven stability analysis is presented for surface patterns on speleothems, i.e., secondary sedimentary cave deposits, by coupling fluid dynamics to the geochemistry of calcite precipitation or dissolution. Falling film theory provides the solution for the flow-field and depth perturbations, the latter being crucial to triggering patterns known as crenulations. In a wide range of Reynolds numbers, the model provides the dominant wavelengths and pattern celerities, in fair agreement with field data. The analysis of the phase velocity of ridges on speleothems has a potential as a proxy of past film flow rates, thus suggesting a new support for paleoclimate analyses.

Eco-morphodynamic carbon pumping by the largest rivers in the Neotropics

The eco-morphodynamic activity of large tropical rivers in South and Central America is analyzed to quantify the carbon flux from riparian vegetation to inland waters. We carried out a multi-temporal analysis of satellite data for all the largest rivers in the Neotropics (i.e, width > 200 m) in the period 2000-2019, at 30 m spatial resolution. We developed a quantification of a highly efficient Carbon Pump mechanism. River morphodynamics is shown to drive carbon export from the riparian zone and to promote net primary production by an integrated process through floodplain rejuvenation and colonization. This pumping mechanism alone is shown to account for 8.9 million tons/year of carbon mobilization in these tropical rivers. We identify signatures of the fluvial eco-morphological activity that provide proxies for the carbon mobilization capability associated with river activity. We discuss river migration-carbon mobilization nexus and effects on the carbon intensity of planned hydroelectric dams in the Neotropics. We recommend that future carbon-oriented water policies on these rivers include a similar analysis.

Convective nature of the planimetric instability in meandering river dynamics

The convective nature of the linear instability of meandering river dynamics is analytically demonstrated and the corresponding Green's function is derived. The wave packet due to impulsive disturbance migrates along a river either downstream or upstream, depending on the subresonant or superresonant conditions. The influence of the parameters that govern the meandering process is shown and the role of the fluid dynamic detail used to describe the morphodynamic problem is discussed. A numerical simulation of the river planimetry is also developed.

A stereoscopic technique for seafloor statistical characterization by acoustic remote sensing

The authors present a new method for performing statistical characterization of underwater surfaces by acoustic remote sensing. A wideband technique is outlined that, by exploiting stereoscopic observation, estimates the roughness height of underwater surfaces however oriented with respect to the instrument. The surface is ensonified by a wideband signal and simultaneously viewed from two or more slightly different directions of view. The corresponding echoes are compared in the frequency domain, and a roughness estimate is obtained. Once the instrument centerband frequency has been fixed, the scale factor in the estimation can be adjusted by varying the differences between the view directions. This permits a wide estimation interval, ranging from a small fraction to many times the wavelength corresponding to the centerband frequency. Preliminary experiments have been carried out in a water tank, and the estimated roughness values are in agreement with the theory.

Flow non-normality-induced transient growth in superposed Newtonian and non-Newtonian fluid layers

In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonian fluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters. In particular, the key role of the density ratio is highlighted.

On the integration of LiDAR and field data for riparian biomass estimation

The role of vegetation in supporting life on Earth is widely known. Nevertheless, the relevance of riparian corridors has been overlooked for a long time, leading to a dramatic reduction of vegetated buffers alongside them. Vegetation monitoring systems, including those for biomass estimation, are required to manage riparian corridors properly. Field surveys may support monitoring, but their usefulness is reduced by numerous drawbacks, therefore needing coupling with other data sources. The present work shows how Light Detection And Ranging (LiDAR) datasets can integrate targeted field measurements to estimate above-ground biomass at temperate or boreal latitudes and generate accurate biomass maps over large areas. By referring to the case study of the Orco river (northwest Italy), we defined a technique to reconstruct the geometry of an individual shrub from LiDAR point clouds. We tested the technique by comparing field measurements with Terrestrial and Airborne Laser Scanner data (TLS and ALS, respectively), assessing the former's superiority but the broader range of applicability of the latter. After these preliminary tests, we coupled the presented technique with a literature algorithm for individual tree detection, providing a more generalized procedure for the overall mapping and budgeting of riparian biomass based on ALS data. We applied the procedure to a fluvial bar of the Orco river, achieving a quantitative assessment of the shrub and tree biomass budget for 2019 and 2021 and visualizing the changes that occurred in that period. These results allowed us to shed light on the prevailing natural and anthropogenic processes in the investigated area and provide insights into the strengths and weaknesses of the proposed procedure.

A global dataset of carbon pumping by the world's largest tropical rivers

The eco-morphodynamic activity of large tropical rivers interacts with riparian vegetation causing implications for the carbon cycle within inland waters. Through a multi-temporal analysis of satellite data spanning the years 2000-2019, we analyzed rivers exceeding 200 m in width across the tropical regions, revealing a Carbon Pump mechanism driving an annual mobilization of 12.45 million tons of organic carbon. The study identifies fluvial eco-morphological signatures as proxies for carbon mobilization, emphasizing the link between river migration and carbon dynamics. To enhance accessibility, our results are encapsulated in a visually compelling WebGIS application, offering a comprehensive understanding of the eco-geomorphological influences on the global carbon cycle within large tropical rivers. Our findings are instrumental in determining the carbon intensity of future hydropower dams, thereby contributing to informed decision-making in the realm of sustainable energy infrastructure. This study elucidates the intricate relationships that govern the nexus of tropical river dynamics, riparian ecosystems, and the global carbon cycle.

Inertial and geometrical effects of self-propelled elliptical Brownian particles

Active particles that self-propel by transforming energy into mechanical motion represent a growing area of research in mathematics, physics, and chemistry. Here we investigate the dynamics of nonspherical inertial active particles moving in a harmonic potential, introducing geometric parameters which take into account the role of eccentricity for nonspherical particles. A comparison between the overdamped and underdamped models for elliptical particles is performed. The model of overdamped active Brownian motion has been used to describe most of the basic aspects of micrometer-sized particles moving in a liquid ("microswimmers"). We consider active particles by extending the active Brownian motion model to incorporate translation and rotation inertia and account for the role of eccentricity. We show how the overdamped and the underdamped models behave in the same way for small values of activity (Brownian case) if eccentricity is equal to zero, but increasing eccentricity leads the two dynamics to substantially depart from each other-in particular, the action of a torque induced by external forces, induced a marked difference close to the walls of the domain if eccentricity is high. Effects induced by inertia include an inertial delay time of the self-propulsion direction from the particle velocity, and the differences between the overdamped and underdamped systems are particularly evident in the first and second moments of the particle velocities. Comparison with the experimental results of vibrated granular particles shows good agreement and corroborates the notion that self-propelling massive particles moving in gaseous media are dominated by inertial effects.