arXiv subjects

Neelesh A. Patankar

Publications and source records attributed to Neelesh A. Patankar.

At least 19 recordsLinked to original sources

arXiv2026

Shapes, forces, and torques of compressed elastic fluid interfaces: beyond axisymmetric configurations

Inspired by the classical Plateau-Douglas problem for soap films bounded by two closed curves, we solve an analogous problem for fluid interfaces with fixed surface area and resistance to out-of-plane bending. The boundaries are planar but need not be symmetric or concentric. The equilibrium surfaces minimize the Willmore bending energy and generalize minimal surfaces such as the catenoid while also exhibiting characteristic features of confined elastic interfaces such as buckling. We systematically classify all possible buckling modes and solution branches by performing a weakly nonlinear analysis and developing a fully nonlinear spectral solver. Our mathematical framework provides insight into the forces and torques required to stabilize cellular membranes and other soft materials and shows that physically relevant asymmetric states can arise even in symmetric systems.

cond-mat.soft↗

arXiv2024

Preventing mass loss in the standard level set method: New insights from variational analyses

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.

physics.flu-dyn↗

arXiv2024

Perspectives on physics-based one-dimensional modeling of lung physiology

The need to understand how infection spreads to the deep lung was acutely realized during the Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) pandemic. The challenge of modeling virus laden aerosol transport and deposition in the airways, coupled with mucus clearance, and infection kinetics, became evident. This perspective provides a consolidated view of coupled one-dimensional physics-based mathematical models to probe multifaceted aspects of lung physiology. Successes of 1D trumpet models in providing mechanistic insights into lung function and optimalities are reviewed while identifying limitations and future directions. Key non-dimensional numbers defining lung function are reported. The need to quantitatively map various pathologies on a physics-based parameter space of non-dimensional numbers (a virtual disease landscape) is noted with an eye on translating modeling to clinical practice. This could aid in disease diagnosis, get mechanistic insights into pathologies, and determine patient specific treatment plan. 1D modeling could be an important tool in developing novel measurement and analysis platforms that could be deployed at point-of-care.

physics.bio-ph↗

arXiv2024

Direct and retrograde signal propagation in unidirectionally coupled Wilson-Cowan oscillators

Certain biological systems exhibit both direct and retrograde propagating wave signals, despite unidirectional neural coupling. However, there is no model to explain this. Therefore, the underlying physics of reversing the signal's direction for one-way coupling remains unclear. Here, we resolve this issue using a Wilson-Cowan oscillators network. By analyzing the limit cycle period of various coupling configurations, we determine that intrinsic frequency differences among oscillators control wave directionality.

physics.bio-ph↗

arXiv2024

Neurological disorders leading to mechanical dysfunction of the esophagus: an emergent behavior of a neuromechanical dynamical system

An understanding how neurological disorders lead to mechanical dysfunction of the esophagus requires knowledge of the neural circuit of the enteric nervous system. Historically, this has been elusive. Here, we present an empirically guided neural circuit for the esophagus. It has a chain of unidirectionally coupled relaxation oscillators, receiving excitatory signals from stretch receptors along the esophagus. The resulting neuromechanical model reveals complex patterns and behaviors that emerge from interacting components in the system. A wide variety of clinically observed normal and abnormal esophageal responses to distension are successfully predicted. Specifically, repetitive antegrade contractions (RACs) are conclusively shown to emerge from the coupled neuromechanical dynamics in response to sustained volumetric distension. Normal RACs are shown to have a robust balance between excitatory and inhibitory neuronal populations, and the mechanical input through stretch receptors. When this balance is affected, contraction patterns akin to motility disorders are observed. For example, clinically observed repetitive retrograde contractions emerge due to a hyper stretch sensitive wall. Such neuromechanical insights could be crucial to eventually develop targeted pharmacological interventions.

q-bio.NC↗

arXiv2024

A unified constraint formulation of immersed body techniques for coupled fluid-solid motion: continuous equations and numerical algorithms

Numerical simulation of moving immersed solid bodies in fluids is now practiced routinely following pioneering work of Peskin and co-workers on immersed boundary method (IBM), Glowinski and co-workers on fictitious domain method (FDM), and others on related methods. A variety of variants of IBM and FDM approaches have been published, most of which rely on using a background mesh for the fluid equations and tracking the solid body using Lagrangian points. The key idea that is common to these methods is to assume that the entire fluid-solid domain is a fluid and then to constrain the fluid within the solid domain to move in accordance with the solid governing equations. The immersed solid body can be rigid or deforming. Thus, in all these methods the fluid domain is extended into the solid domain. In this review, we provide a mathemarical perspective of various immersed methods by recasting the governing equations in an extended domain form for the fluid. The solid equations are used to impose appropriate constraints on the fluid that is extended into the solid domain. This leads to extended domain constrained fluid-solid governing equations that provide a unified framework for various immersed body techniques. The unified constrained governing equations in the strong form are independent of the temporal or spatial discretization schemes. We show that particular choices of time stepping and spatial discretization lead to different techniques reported in literature ranging from freely moving rigid to elastic self-propelling bodies. These techniques have wide ranging applications including aquatic locomotion, underwater vehicles, car aerodynamics, and organ physiology (e.g. cardiac flow, esophageal transport, respiratory flows), wave energy convertors, among others. We conclude with comments on outstanding challenges and future directions.

math.NA↗

arXiv2023

The physical origin of aneurysm growth, dissection, and rupture

Rupture of aortic aneurysms is by far the most fatal heart disease, with a mortality rate exceeding 80%. There are no reliable clinical protocols to predict growth, dissection, and rupture because the fundamental physics driving aneurysm progression is unknown. Here, via in-vitro experiments, we show that a blood-wall, fluttering instability manifests in synthetic arteries under pulsatile forcing. We establish a phase space to prove that the transition from stable flow to unstable aortic flutter is accurately predicted by a flutter instability parameter derived from first principles. Time resolved strain maps of the evolving system reveal the dynamical characteristics of aortic flutter that drive aneurysm progression. We show that low level instability can trigger permanent aortic growth, even in the absence of material remodeling. Sufficiently large flutter beyond a secondary threshold localizes strain in the walls to the length scale clinically observed in aortic dissection. Lastly, significant physical flutter beyond a tertiary threshold can ultimately induce aneurysm rupture via failure modes reported from necropsy. Resolving the fundamental physics of aneurysm progression directly leads to clinical protocols that forecast growth as well as intercept dissection and rupture by pinpointing their physical origin.

q-bio.TO↗

arXiv2023

Fluid-structure instability forecasts thoracic aortic aneurysm progression

The basic mechanism driving aneurysm growth is unknown. Currently, clinical diagnosis of an aneurysm is mainly informed by retrospective tracking of its size and growth rate. However, aneurysms can rupture before reactive criteria are met or remain stable when they are exceeded. Here, we identify a fluid-structure instability that is associated with abnormal aortic dilatation. Our analysis yields a measurable dimensionless number and its analytically derived critical threshold. This threshold pinpoints the transition from stable flow to unstable aortic fluttering as a function of the physiological properties composing the dimensionless number, like blood pressure and aortic compliance. A retrospective study was then conducted with 4D-flow MRI data from 117 patients indicated for cardiac imaging and 100 healthy volunteers recruited prospectively. The difference between the dimensionless number and its critical threshold was calculated for every subject from their earliest MRI data and used as an aneurysm physiomarker to forecast future growth. As a binary predictor for abnormal growth and subsequent surgical intervention reported from follow-up imaging, the aneurysm physiomarker yielded an AUC of 0.997 in a receiving operator characteristic analysis. Though validated here for thoracic ascending aortic aneurysms, this instability mechanism may be used to understand, predict and inform patient-specific treatment of aneurysms in any location without fundamental differences.

physics.med-ph↗

arXiv2022

Directional self-propelled transport of coalesced droplets on a superhydrophilic cylindrical wire

Droplets coalescing on flat surfaces tend to end up with the smaller droplet migrating into the larger one. We report a counter-intuitive droplet coalescence pattern on a superhydrophilic cylindrical wire, where the larger droplet is pulled toward the smaller one. Consequently, the center of the combined mass significantly moves toward, often beyond, the original location of the smaller droplet. This phenomenon occurs primarily because the viscous friction that a droplet experiences on a cylindrical wire is not positively correlated with the size of the droplet, unlike the droplets coalescing on flat surfaces. We conducted a dimensional analysis based on a mass-spring-damper (MSD) model. Our model predicts a variety of coalescence patterns as a function of the ratio between droplet sizes, and the prediction matches the experimental observation.

physics.flu-dyn↗

arXiv2022

Self-sustained oscillations in whiskers without vortex shedding

Sensing the flow of water or air disturbance is critical for the survival of many animals: flow information helps them localize food, mates, and prey and to escape predators. Across species, many flow sensors take the form of long, flexible cantilevers. These cantilevers are known to exhibit sustained oscillations when interacting with fluid flow. In the presence of vortex shedding, the oscillations occur through mechanisms such as wake- or vortex-induced vibrations. There is, however, no clear explanation for the mechanisms governing the sustained oscillation of flexible cantilevers without vortex shedding. In recent work, we showed that a flexible cylindrical cantilever could experience sustained oscillations in its first natural vibration mode in water at Reynolds numbers below the critical Reynolds number of vortex shedding. The oscillations were shown to be driven by a frequency match (synchronization) between the flow frequency and the cantilever's first-mode natural frequency. Here, we use a body-fitted fluid-structure solver based on the Navier-Stokes and nonlinear structural equations to simulate the dynamics of a cantilevered whisker in the air at a subcritical value of Reynolds number. Results show that second-mode synchronization governs the whisker's sustained oscillation. Wavy patterns in the shear layer dominate the whisker's wake during the vibrations, indicating that parallel shear layers synchronize with the whisker's motion. As a result of this synchronization, oval-shaped motion trajectories, with matching streamwise and cross-flow vibration frequencies, are observed along the whisker. The outcomes of this study suggest possible directions for designing artificial bio-inspired flow sensors.

physics.flu-dyn↗

arXiv2022

A mechanics--based perspective on the function of human sphincters during functional luminal imaging probe manometry

Functional luminal imaging probe (FLIP) is used to measure cross-sectional area (CSA) and pressure at sphincters. It consists of a catheter surrounded by a fluid filled cylindrical bag, closed on both ends. Plotting the pressure-CSA hysteresis of a sphincter during a contraction cycle, which is available through FLIP testing, offers information on its functionality, and can provide diagnostic insights. However, limited work has been done to explain the mechanics of these pressure-CSA loops. This work presents a consolidated picture of pressure-CSA loops of different sphincters. Clinical data reveal that although sphincters have a similar purpose (controlling the flow of liquids and solids by opening and closing), two different pressure-CSA loop patterns emerge: negative slope loop (NSL) and positive slope loop (PSL). We show that the loop type is the result of an interplay between (or lack thereof) two mechanical modes: (i) neurogenic mediated relaxation of the sphincter muscle and (ii) muscle contraction proximal to the sphincter which causes mechanical distention. We conclude that sphincters which only function through mechanism (i) exhibition NSL whereas sphincters which open as a result of both (i) and (ii) display a PSL. This work provides a fundamental mechanical understanding of human sphincters. This can be used to identify normal and abnormal phenotypes for the different sphincters and help in creating physiomarkers based on work calculation.

physics.med-ph↗

arXiv2022

MRI-MECH: Mechanics-informed MRI to estimate esophageal health

Dynamic magnetic resonance imaging (MRI) is a popular medical imaging technique to generate image sequences of the flow of a contrast material inside tissues and organs. However, its application to imaging bolus movement through the esophagus has only been demonstrated in few feasibility studies and is relatively unexplored. In this work, we present a computational framework called mechanics-informed MRI (MRI-MECH) that enhances that capability thereby increasing the applicability of dynamic MRI for diagnosing esophageal disorders. Pineapple juice was used as the swallowed contrast material for the dynamic MRI and the MRI image sequence was used as input to the MRI-MECH. The MRI-MECH modeled the esophagus as a flexible one-dimensional tube and the elastic tube walls followed a linear tube law. Flow through the esophagus was then governed by one-dimensional mass and momentum conservation equations. These equations were solved using a physics-informed neural network (PINN). The PINN minimized the difference between the measurements from the MRI and model predictions ensuring that the physics of the fluid flow problem was always followed. MRI-MECH calculated the fluid velocity and pressure during esophageal transit and estimated the mechanical health of the esophagus by calculating wall stiffness and active relaxation. Additionally, MRI-MECH predicted missing information about the lower esophageal sphincter during the emptying process, demonstrating its applicability to scenarios with missing data or poor image resolution. In addition to potentially improving clinical decisions based on quantitative estimates of the mechanical health of the esophagus, MRI-MECH can also be enhanced for application to other medical imaging modalities to enhance their functionality as well.

physics.med-ph↗

arXiv2022

Pulmonary drug delivery and retention: a computational study to identify plausible parameters based on a coupled airway-mucus flow model

Pulmonary drug delivery systems rely on inhalation of drug-laden aerosols produced from aerosol generators such as inhalers, nebulizers etc. On deposition, the drug molecules diffuse in the mucus layer and are also subjected to mucociliary advection which transports the drugs away from the initial deposition site. The availability of the drug at a particular region of the lung is, thus, determined by a balance between these two phenomena. A mathematical analysis of drug deposition and retention in the lungs is developed through a coupled mathematical model of aerosol transport in air as well as drug molecule transport in the mucus layer. The mathematical model is solved computationally to identify suitable conditions for the transport of drug-laden aerosols to the deep lungs. This study identifies the conditions conducive for delivering drugs to the deep lungs which is crucial for achieving systemic drug delivery. The effect of different parameters on drug retention is also characterized for various regions of the lungs, which is important in determining the availability of the inhaled drugs at a target location. Our analysis confirms that drug delivery efficacy remains highest for aerosols in the size range of 1-5 $μ$m. Moreover, it is observed that amount of drugs deposited in the deep lung increases by a factor of 2 when the breathing time period is doubled, with respect to normal breathing, suggesting breath control as a means to increase the efficacy of drug delivery to the deep lung. A higher efficacy also reduces the drug load required to be inhaled to produce the same health effects and hence, can help in minimizing the side effects of a drug.

q-bio.TO↗

arXiv2022

Pressure -- area loop based phenotypic classification and mechanics of esophagogastric junction physiology

The esophagogastric junction (EGJ) is located at the distal end of the esophagus and acts as a valve allowing swallowed materials to enter the stomach and preventing acid reflux. Irregular weakening or stiffening of the EGJ muscles result in changes to its opening and closing patterns which can progress into esophageal disorders. Therefore, understanding the physics behind the opening and closing cycle of the EGJ provides a mechanistic insight into its function and can help identify the underlying conditions that cause its degradation. Using clinical FLIP data, we plotted the pressure-area hysteresis at the EGJ location and distinguished two major loop types, a pressure dominant loop (PDL) and a tone dominant loop (TDL). In this study, we aimed to identify the key characteristics that define each loop type and find what causes the inversion from one loop to another. To do so, the clinical observations were reproduced using 1D simulations of flow inside a FLIP device located in the esophagus, and the work done by the EGJ wall over time was calculated. This work was decomposed into active and passive components, which revealed the competing mechanisms that dictate the loop type. These mechanisms are esophagus stiffness, fluid viscosity, and the EGJ relaxation pattern. In PDL, the leading source of energy in the cycle is coming from the fluid pressure increase from the peristaltic contraction wave, and in TDL the leading source of energy in the cycle is coming from the contraction and relaxation of the EGJ tone.

physics.bio-ph↗

arXiv2021

Peristaltic regimes in esophageal transport

A FLIP device gives cross-sectional area along the length of the esophagus and one pressure measurement, both as a function of time. Deducing mechanical properties of the esophagus including wall material properties, contraction strength, and wall relaxation from these data is a challenging inverse problem. Knowing mechanical properties can change how clinical decisions are made because of its potential for in-vivo mechanistic insights. To obtain such information, we conducted a parametric study to identify peristaltic regimes by using a 1D model of peristaltic flow through an elastic tube closed on both ends and also applied it to interpret clinical data. The results gave insightful information about the effect of tube stiffness, fluid/bolus density and contraction strength on the resulting esophagus shape through quantitive representations of the peristaltic regimes. Our analysis also revealed the mechanics of the opening of the contraction area as a function of bolus flow resistance. Lastly, we concluded that peristaltic driven flow displays three modes of peristaltic geometries, but all physiologically relevant flows fall into two peristaltic regimes characterized by a tight contraction.

physics.flu-dyn↗

arXiv2021

Esophageal virtual disease landscape using mechanics-informed machine learning

The pathogenesis of esophageal disorders is related to the esophageal wall mechanics. Therefore, to understand the underlying fundamental mechanisms behind various esophageal disorders, it is crucial to map the esophageal wall mechanics-based parameters onto physiological and pathophysiological conditions corresponding to altered bolus transit and supraphysiologic IBP. In this work, we present a hybrid framework that combines fluid mechanics and machine learning to identify the underlying physics of the various esophageal disorders and maps them onto a parameter space which we call the virtual disease landscape (VDL). A one-dimensional inverse model processes the output from an esophageal diagnostic device called endoscopic functional lumen imaging probe (EndoFLIP) to estimate the mechanical "health" of the esophagus by predicting a set of mechanics-based parameters such as esophageal wall stiffness, muscle contraction pattern and active relaxation of esophageal walls. The mechanics-based parameters were then used to train a neural network that consists of a variational autoencoder (VAE) that generates a latent space and a side network that predicts mechanical work metrics for estimating esophagogastric junction motility. The latent vectors along with a set of discrete mechanics-based parameters define the VDL and form clusters corresponding to the various esophageal disorders. The VDL not only distinguishes different disorders but can also be used to predict disease progression in time. Finally, we also demonstrate the clinical applicability of this framework for estimating the effectiveness of a treatment and track patient condition after a treatment.

cs.LG↗

arXiv2021

Handling Neumann and Robin boundary conditions in a fictitious domain volume penalization framework

Sakurai et al. (J Comput Phys, 2019) presented a flux-based volume penalization (VP) approach for imposing inhomogeneous Neumann boundary conditions on embedded interfaces. The flux-based VP method modifies the diffusion coefficient of the original elliptic (Poisson) equation and uses a flux-forcing function as a source term in the equation to impose the Neumann boundary conditions. As such, the flux-based VP method can be easily incorporated into existing fictitious domain codes. Sakurai et al. relied on an analytical construction of flux-forcing functions, which limits the practicality of the approach. Because of the analytical approach taken in the prior work, only (spatially) constant flux values on simple interfaces were considered. In this paper, we present a numerical technique for constructing flux-forcing functions for arbitrarily complex boundaries. The imposed flux values are also allowed to vary spatially in our approach. Furthermore, the flux-based VP method is extended to include (spatially varying) Robin boundary conditions, which makes the flux-based VP method even more general. We consider several two- and three-dimensional test examples to access the spatial accuracy of the numerical solutions. The method is also used to simulate flux-driven thermal convection in a concentric annular domain. We formally derive the flux-based volume penalized Poisson equation satisfying Neumann/Robin boundary condition in strong form; such a derivation was not presented in Sakurai et al., where the equation first appeared for the Neumann problem. The derivation reveals that the flux-based VP approach relies on a surface delta function to impose inhomogeneous Neumann/Robin boundary conditions. However, explicit construction of the delta function is not necessary for the flux-based VP method, which makes it different from other diffuse domain equations presented in the literature.

math.NA↗

arXiv2021

A Fully Resolved Multiphysics Model of Gastric Peristalsis and Bolus Emptying in the Upper Gastrointestinal Tract

Over the past few decades, in silico modeling of organ systems has significantly furthered our understanding of their physiology and biomechanical function. In this work, we present a detailed numerical model of the upper gastrointestinal (GI) tract that not only accounts for the fiber architecture of the muscle walls, but also the multiphasic components they help transport during normal digestive function. Construction details for 3D models of representative stomach geometry are presented along with a simple strategy for assigning circular and longitudinal muscle fiber orientations for each layer. Based on our previous work that created a fully resolved model of esophageal peristalsis, we extend the same principles to simulate gastric peristalsis by systematically activating muscle fibers embedded in the stomach. Following this, for the first time, we simulate gravity driven bolus emptying into the stomach due to density differences between ingested contents and fluid contents of the stomach. This detailed computational model of the upper gastrointestinal tract provides a foundation on which future models can be based that seek to investigate the biomechanics of acid reflux and probe various strategies for gastric bypass surgeries to address the growing problem of adult obesity.

physics.flu-dyn↗