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He Y, Battista NA, Waldrop LD. Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory. J Math Biol 2024; 89:13. [PMID: 38879850 DOI: 10.1007/s00285-024-02116-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 05/22/2024] [Accepted: 06/04/2024] [Indexed: 06/28/2024]
Abstract
In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.
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Affiliation(s)
- Yanyan He
- Department of Mathematics, and of Computer Science and Engineering, University of North Texas, 1155 Union Circle, Denton, TX, 76203, USA.
| | - Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, Pennington Rd, Ewing Township, NJ, 08618, USA
| | - Lindsay D Waldrop
- Schmid College of Science and Technology, Chapman University, One University Drive, Orange, CA, 92866, USA
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2
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Kodirov SA. Probability that there is a mammalian counterpart of cardiac clock in insects. ARCHIVES OF INSECT BIOCHEMISTRY AND PHYSIOLOGY 2022; 110:e21867. [PMID: 35106839 PMCID: PMC9250754 DOI: 10.1002/arch.21867] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 12/25/2021] [Indexed: 05/05/2023]
Abstract
Whether or not the hyperpolarization-activated cyclic nucleotide-gated nonselective cation channel (HCN or funny current If ) is involved in pacemaking - recurrent heartbeat, it is attributed to electrical activities in all excitable cells, including those of invertebrates. In latter group of animals prevailingly the electrical signals and function of heart in terms of chrono- and inotropy are elucidated. Although in simpler models including insects experimental outcomes are reproducible and robust, involvement of "cardiac clock" mechanism in pacemaking is not conclusive. In this assay, the mechanisms of heartbeat are synthesized by focused comparisons between insect and mammalian hearts.
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Affiliation(s)
- Sodikdjon A. Kodirov
- Pavlov Institute of Physiology, Russian Academy of Sciences, Saint Petersburg, Russia
- Department of Biological Sciences, University of Texas at Brownsville, Brownsville, Texas, USA
- Instituto de Medicina Molecular, Universidade de Lisboa, Lisbon, Portugal
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Soni T, Sharma A, Dutta R, Dutta A, Jayavelu S, Sarkar S. Capturing functional relations in fluid-structure interaction via machine learning. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220097. [PMID: 35401993 PMCID: PMC8984386 DOI: 10.1098/rsos.220097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
While fluid-structure interaction (FSI) problems are ubiquitous in various applications from cell biology to aerodynamics, they involve huge computational overhead. In this paper, we adopt a machine learning (ML)-based strategy to bypass the detailed FSI analysis that requires cumbersome simulations in solving the Navier-Stokes equations. To mimic the effect of fluid on an immersed beam, we have introduced dissipation into the beam model with time-varying forces acting on it. The forces in a discretized set-up have been decoupled via an appropriate linear algebraic operation, which generates the ground truth force/moment data for the ML analysis. The adopted ML technique, symbolic regression, generates computationally tractable functional forms to represent the force/moment with respect to space and time. These estimates are fed into the dissipative beam model to generate the immersed beam's deflections over time, which are in conformity with the detailed FSI solutions. Numerical results demonstrate that the ML-estimated continuous force and moment functions are able to accurately predict the beam deflections under different discretizations.
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Affiliation(s)
- Tejas Soni
- Department of Civil Engineering, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India
| | - Ashwani Sharma
- Department of Civil Engineering, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India
| | - Rajdeep Dutta
- Department of Machine Intellection, Institute for Infocomm Research Technology and Research Agency for Science, Singapore, Singapore
| | - Annwesha Dutta
- ICTP - The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste 34151, Italy
- Department of Physics, Indian Institute of Science Education and Research, Tirupati 517507, India
| | - Senthilnath Jayavelu
- Department of Machine Intellection, Institute for Infocomm Research Technology and Research Agency for Science, Singapore, Singapore
| | - Saikat Sarkar
- Department of Civil Engineering, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India
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Sharifi A, Gendernalik A, Garrity D, Bark D. Valveless pumping behavior of the simulated embryonic heart tube as a function of contractile patterns and myocardial stiffness. Biomech Model Mechanobiol 2021; 20:2001-2012. [PMID: 34297252 DOI: 10.1007/s10237-021-01489-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 06/29/2021] [Indexed: 10/20/2022]
Abstract
During development, the heart begins pumping as a valveless multilayered tube capable of driving blood flow throughout the embryonic vasculature. The mechanical properties and how they interface with pumping function are not well-defined at this stage. Here, we evaluate pumping patterns using a fluid-structure interaction computational model, combined with experimental data and an energetic analysis to investigate myocardial mechanical properties. Through this work, we propose that a myocardium modeled as a Neo-Hookean material with a material constant on the order of 10 kPa is necessary for the heart tube to function with an optimal pressure and cardiac output.
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Affiliation(s)
- Alireza Sharifi
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA
| | - Alex Gendernalik
- Department of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA
| | - Deborah Garrity
- Department of Biology, Colorado State University, Fort Collins, CO, USA
| | - David Bark
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA. .,Department of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA. .,Department of Pediatrics, Washington University in St. Louis, St. Louis, MO, USA.
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Waldrop LD, He Y, Battista NA, Neary Peterman T, Miller LA. Uncertainty quantification reveals the physical constraints on pumping by peristaltic hearts. J R Soc Interface 2020; 17:20200232. [PMID: 32900306 DOI: 10.1098/rsif.2020.0232] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Most biological functional systems are complex, and this complexity is a fundamental driver of diversity. Because input parameters interact in complex ways, a holistic understanding of functional systems is key to understanding how natural selection produces diversity. We present uncertainty quantification (UQ) as a quantitative analysis tool on computational models to study the interplay of complex systems and diversity. We investigate peristaltic pumping in a racetrack circulatory system using a computational model and analyse the impact of three input parameters (Womersley number, compression frequency, compression ratio) on flow and the energetic costs of circulation. We employed two models of peristalsis (one that allows elastic interactions between the heart tube and fluid and one that does not), to investigate the role of elastic interactions on model output. A computationally cheaper surrogate of the input parameter space was created with generalized polynomial chaos expansion to save computational resources. Sobol indices were then calculated based on the generalized polynomial chaos expansion and model output. We found that all flow metrics were highly sensitive to changes in compression ratio and insensitive to Womersley number and compression frequency, consistent across models of peristalsis. Elastic interactions changed the patterns of parameter sensitivity for energetic costs between the two models, revealing that elastic interactions are probably a key physical metric of peristalsis. The UQ analysis created two hypotheses regarding diversity: favouring high flow rates (where compression ratio is large and highly conserved) and minimizing energetic costs (which avoids combinations of high compression ratios, high frequencies and low Womersley numbers).
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Affiliation(s)
- Lindsay D Waldrop
- Schmid College of Science and Technology, Chapman University, 1 University Drive, Orange, CA 92866, USA
| | - Yanyan He
- Department of Mathematics, University of North Texas, Denton, TX 76203, USA.,Department of Computer Science and Engineering, University of North Texas, Denton, TX 76203, USA
| | - Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, Ewing Township, NJ 08628, USA
| | - Tess Neary Peterman
- Department of Biology, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
| | - Laura A Miller
- Department of Mathematics, University of Arizona, Tuscon, AZ 85721, USA
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Collective Pulsing in Xeniid Corals: Part II-Using Computational Fluid Dynamics to Determine if There are Benefits to Coordinated Pulsing. Bull Math Biol 2020; 82:67. [PMID: 32474651 DOI: 10.1007/s11538-020-00741-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 04/23/2020] [Indexed: 10/24/2022]
Abstract
Coordinated movements have been shown to enhance the speed or efficiency of swimming, flying, and pumping in many organisms. Coordinated pulsing has not been observed in many cnidarians (jellyfish, anemones, corals), as is the case for the xeniid corals considered in our corresponding paper. This observation opens the question as to whether xeniid corals, and cnidarians in general, do not coordinate their pulsing behavior for lack of a hydrodynamic advantage or for other reasons. For example, a diffuse nervous system with lack of substantial sensory input may not be capable of such coordination. Similarly, grouping may serve a defensive role rather than a fluid dynamic role. In this paper, the immersed boundary method is used to quantify the volumetric flux of fluid generated by an individual xeniid coral polyp in comparison with a pair of polyps. Both the distances between the polyps and the phase difference between each polyp are considered. More specifically, the fully coupled fluid-structure interaction problem of a coral polyp driving fluid flow is solved using a hybrid version of the immersed boundary method where the Navier-Stokes equations are solved using a finite differences and the elasticity equations describing the coral are solved using finite elements. We explore three possible hypotheses: (1) pulsing in pairs increases upward flow above the polyps and is thus beneficial, (2) these benefits vary with the polyps' pulsing phase difference, and (3) these benefits vary with the distance between the polyps. We find that there is no substantial hydrodynamic advantage to pulsing in a pair for any phase difference. The volumetric flux of fluid generated by each coral also decreases as the distance between polyps is decreased. This surprising result is consistent with measurements taken from another cnidarian with similar behavior, the upside down jellyfish, in which each medusa drives less flow when in a group.
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