Channelization cascade in landscape evolution.

The hierarchy of channel networks in landscapes displays features that are characteristic of nonequilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial differential equations coupling landscape evolution dynamics with a specific catchment area equation. By means of a linear stability analysis we identify the critical conditions triggering channel formation and the emergence of characteristic valley spacing. The ensuing channelization cascade, described by a dimensionless number accounting for diffusive soil creep, runoff erosion, and tectonic uplift, is reminiscent of the subsequent instabilities in fluid turbulence, while the structure of the simulated patterns is indicative of a tendency to evolve toward optimal configurations, with anomalies similar to dislocation defects observed in pattern-forming systems. The choice of specific geomorphic transport laws and boundary conditions strongly influences the channelization cascade, underlying the nonlocal and nonlinear character of its dynamics.

Parametric transitions between bare and vegetated states in water-driven patterns.

Conditions for vegetation spreading and pattern formation are mathematically framed through an analysis encompassing three fundamental processes: flow stochasticity, vegetation dynamics, and sediment transport. Flow unsteadiness is included through Poisson stochastic processes whereby vegetation dynamics appears as a secondary instability, which is addressed by Floquet theory. Results show that the model captures the physical conditions heralding the transition between bare and vegetated fluvial states where the nonlinear formation and growth of finite alternate bars are accounted for by Center Manifold Projection. This paves the way to understand changes in biogeomorphological styles induced by man in the Anthropocene and of natural origin since the Paleozoic (Devonian plant hypothesis).

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.

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.

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.

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.

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.

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.

Non-invasive aortic systolic pressure and pulse wave velocity estimation in a primary care setting: An in silico study.

Everyday clinical cardiovascular evaluation is still largely based on brachial systolic and diastolic pressures. However, several clinical studies have demonstrated the higher diagnostic capacities of the aortic pressure, as well as the need to assess the aortic mechanical properties (e.g., by measuring the aortic pulse wave velocity). In order to fill this gap, we propose to exploit a set of easy-to-obtain physical characteristics to estimate the aortic pressure and pulse wave velocity. To this aim, a large population of virtual subjects is created by a validated mathematical model of the cardiovascular system. Quadratic regressive models are then fitted and statistically selected in order to obtain reliable estimations of the aortic pressure and pulse wave velocity starting from the knowledge of the subject age, height, weight, brachial pressure, photoplethysmographic measures and either electrocardiogram or phonocardiogram. The results are very encouraging and foster clinical studies aiming to apply a similar technique to a real population.

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.

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.

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.

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

[This corrects the article DOI: 10.1371/journal.pone.0151523.].

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.

Modelling and subject-specific validation of the heart-arterial tree system.

A modeling approach integrated with a novel subject-specific characterization is here proposed for the assessment of hemodynamic values of the arterial tree. A 1D model is adopted to characterize large-to-medium arteries, while the left ventricle, aortic valve and distal micro-circulation sectors are described by lumped submodels. A new velocity profile and a new formulation of the non-linear viscoelastic constitutive relation suitable for the {Q, A} modeling are also proposed. The model is firstly verified semi-quantitatively against literature data. A simple but effective procedure for obtaining subject-specific model characterization from non-invasive measurements is then designed. A detailed subject-specific validation against in vivo measurements from a population of six healthy young men is also performed. Several key quantities of heart dynamics-mean ejected flow, ejection fraction, and left-ventricular end-diastolic, end-systolic and stroke volumes-and the pressure waveforms (at the central, radial, brachial, femoral, and posterior tibial sites) are compared with measured data. Mean errors around 5 and 8%, obtained for the heart and arterial quantities, respectively, testify the effectiveness of the model and its subject-specific characterization.

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.

Impact of atrial fibrillation on the cardiovascular system through a lumped-parameter approach.

Atrial fibrillation (AF) is the most common arrhythmia affecting millions of people in the Western countries and, due to the widespread impact on the population and its medical relevance, is largely investigated in both clinical and bioengineering sciences. However, some important feedback mechanisms are still not clearly established. The present study aims at understanding the global response of the cardiovascular system during paroxysmal AF through a lumped-parameter approach, which is here performed paying particular attention to the stochastic modeling of the irregular heartbeats and the reduced contractility of the heart. AF can be here analyzed by means of a wide number of hemodynamic parameters and avoiding the presence of other pathologies, which usually accompany AF. Reduced cardiac output with correlated drop of ejection fraction and decreased amount of energy converted to work by the heart during blood pumping, as well as higher left atrial volumes and pressures are some of the most representative results aligned with the existing clinical literature and here emerging during acute AF. The present modeling, providing new insights on cardiovascular variables which are difficult to measure and rarely reported in literature, turns out to be an efficient and powerful tool for a deeper comprehension and prediction of the arrythmia impact on the whole cardiovascular system.