Special Issue "Mathematical Modeling in Biomechanics and Mechanobiology"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 7108

Special Issue Editors

Prof. Dr. Alessio Gizzi
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Guest Editor
Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, 00128 Rome, Italy
Interests: continuum biomechanics; mathematical modeling; computational biology
Prof. Dr. Michele Marino
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Guest Editor
Institute of Continuum Mechanics, Leibniz University Hannover, 11 30167 Appelstr, Germany
Interests: continuum mechanics; constitutive modeling; multiscale analyses
Prof. Dr. Giuseppe Vairo
E-Mail Website
Guest Editor
Department of Civil Engineering and Computer Science, University of Rome “Tor Vergata”, via del Politecnico 1, 001133 Rome, Italy
Interests: continuum mechanics; constitutive modeling; multiscale analyses; biomechanics

Special Issue Information

Dear Colleagues,

State-of-the-art problems of the biomedical research-based industry require multidisciplinary skills in merging complementary knowledge from different fields. The critical thinking of biomechanics and mechanobiology applications provides the right emphasis to handle scientific and technological challenges able to foster an effective translation towards the clinical world. In such a scenario, biomedical imaging, theoretical biology, biomechanics, mechanobiology, computational modeling, and numerical simulation are all necessary ingredients of such complex challenging problems. A solid international network on theoretical and applied biomechanics provides the fecund humus in which young scientists can find their research line in a robust epistemological framework.

The purpose of this Special Issue is to gather a collection of articles reflecting the state-of-the-art in different fields of Mathematical Modeling in Biomechanics and Mechanobiology, offering a wide and rigorous perspective. New synergies are needed to face the urgent challenges connected with healthcare social problems and sustainability through integrated multidisciplinary approaches. This special issue is linked to the Advanced International School on “Imaging, Modeling and Simulation in Biomechanics and Mechanobiology” (http://www.unicampus.it/eng/current/imaging-modeling-and-simulation-in-biomechanics-mechanobiology).

Prof. Dr. Alessio Gizzi
Prof. Dr. Michele Marino
Prof. Dr. Giuseppe Vairo
Guest Editors

Manuscript Submission Information

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Keywords

  • Mathematical modeling
  • Biomechanics
  • Mechanobiology
  • Biomedical imaging
  • Continuum mechanics
  • Theoretical biology
  • Computational modeling
  • Numerical modeling

Published Papers (6 papers)

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Research

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Article
Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation
Mathematics 2021, 9(2), 164; https://doi.org/10.3390/math9020164 - 14 Jan 2021
Cited by 5 | Viewed by 1134
Abstract
The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of [...] Read more.
The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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Article
Inelastic Deformable Image Registration (i-DIR): Capturing Sliding Motion through Automatic Detection of Discontinuities
Mathematics 2021, 9(1), 97; https://doi.org/10.3390/math9010097 - 05 Jan 2021
Viewed by 889
Abstract
Deformable image registration (DIR) is an image-analysis method with a broad range of applications in biomedical sciences. Current applications of DIR on computed-tomography (CT) images of the lung and other organs under deformation suffer from large errors and artifacts due to the inability [...] Read more.
Deformable image registration (DIR) is an image-analysis method with a broad range of applications in biomedical sciences. Current applications of DIR on computed-tomography (CT) images of the lung and other organs under deformation suffer from large errors and artifacts due to the inability of standard DIR methods to capture sliding between interfaces, as standard transformation models cannot adequately handle discontinuities. In this work, we aim at creating a novel inelastic deformable image registration (i-DIR) method that automatically detects sliding surfaces and that is capable of handling sliding discontinuous motion. Our method relies on the introduction of an inelastic regularization term in the DIR formulation, where sliding is characterized as an inelastic shear strain. We validate the i-DIR by studying synthetic image datasets with strong sliding motion, and compare its results against two other elastic DIR formulations using landmark analysis. Further, we demonstrate the applicability of the i-DIR method to medical CT images by registering lung CT images. Our results show that the i-DIR method delivers accurate estimates of a local lung strain that are similar to fields reported in the literature, and that do not exhibit spurious oscillatory patterns typically observed in elastic DIR methods. We conclude that the i-DIR method automatically locates regions of sliding that arise in the dorsal pleural cavity, delivering significantly smaller errors than traditional elastic DIR methods. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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Article
On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts
Mathematics 2020, 8(12), 2242; https://doi.org/10.3390/math8122242 - 18 Dec 2020
Cited by 5 | Viewed by 1279
Abstract
Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of [...] Read more.
Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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Article
Analysis of the Upper Limitation of the Most Convenient Cadence Range in Cycling Using an Equivalent Moment Based Cost Function
Mathematics 2020, 8(11), 1947; https://doi.org/10.3390/math8111947 - 04 Nov 2020
Viewed by 600
Abstract
The article presents the study of the pedalling rates obtained by minimizing a cost function based on a kinetic approach and which can be estimated with more easily achievable experimental data as input than other cost functions. Simulations based on data available in [...] Read more.
The article presents the study of the pedalling rates obtained by minimizing a cost function based on a kinetic approach and which can be estimated with more easily achievable experimental data as input than other cost functions. Simulations based on data available in the literature were used to compare the cadences obtained by minimizing well-known joint moment-based cost functions and the proposed cost function. The influence of the power output and of the body mass index on the pedalling rates that minimize the cost function was investigated. Experimental tests performed by four competitive cyclists in the field were used as comparison for the results based on simulations. From simulations emerged that results obtained with the cost function proposed in this work were similar to those based on the absolute average joint moments. We found that the upper limit of the more convenient pedalling rate range decreases linearly with the body mass index, while it increases non-linearly with power output. Furthermore, a polynomial regression of the correlation of the pedalling rate obtained through the method and body mass index and power was found. Experimental results confirmed that the proposed model, finding an approximation of the minimum of muscular effort (not including negative muscular work), is able to estimate the upper limit of an optimal range of cadence. All tested cyclists freely choose to pedal at a cadence under this limit. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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Article
Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method
Mathematics 2020, 8(6), 917; https://doi.org/10.3390/math8060917 - 04 Jun 2020
Cited by 2 | Viewed by 1367
Abstract
This paper discusses the torque data during Parachute Landing Fall (PLF) activity on the sagittal plane by applying Kane’s method. The value of torque is determined in order to identify the movement of extension and flexion at every joint-segment on the parachutist during [...] Read more.
This paper discusses the torque data during Parachute Landing Fall (PLF) activity on the sagittal plane by applying Kane’s method. The value of torque is determined in order to identify the movement of extension and flexion at every joint-segment on the parachutist during landing. Data were obtained from three professional and eighteen amateur parachutists, each with three consecutive landings. Quintic Biomechanics Software v26 was selected to capture motion analysis. The mathematical model for the PLF technique was presented based on a two-link kinematics open chain in a two-dimensional space using Kane’s method. The t-test result showed the p-value of torque at each joint between professionals and amateurs (p ≤ 0.05). According to the torque result, the professional parachutists extended their arm then flexion their elbow, shoulder, hip, knee and the ankle plantar flexion during the foot strike phase. The professional demonstrated a perfect PLF technique by identifying the flexion and extension on each joint segment that was involved during landing activity. The value of torque at each joint segment from professional parachutists may be used as a guideline for amateurs to perform optimal landing and minimise the injury. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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Review

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Review
Biophysics and Modeling of Mechanotransduction in Neurons: A Review
Mathematics 2021, 9(4), 323; https://doi.org/10.3390/math9040323 - 06 Feb 2021
Cited by 3 | Viewed by 1054
Abstract
Mechanosensing is a key feature through which organisms can receive inputs from the environment and convert them into specific functional and behavioral outputs. Mechanosensation occurs in many cells and tissues, regulating a plethora of molecular processes based on the distribution of forces and [...] Read more.
Mechanosensing is a key feature through which organisms can receive inputs from the environment and convert them into specific functional and behavioral outputs. Mechanosensation occurs in many cells and tissues, regulating a plethora of molecular processes based on the distribution of forces and stresses both at the cell membrane and at the intracellular organelles levels, through complex interactions between cells’ microstructures, cytoskeleton, and extracellular matrix. Although several primary and secondary mechanisms have been shown to contribute to mechanosensation, a fundamental pathway in simple organisms and mammals involves the presence of specialized sensory neurons and the presence of different types of mechanosensitive ion channels on the neuronal cell membrane. In this contribution, we present a review of the main ion channels which have been proven to be significantly involved in mechanotransduction in neurons. Further, we discuss recent studies focused on the biological mechanisms and modeling of mechanosensitive ion channels’ gating, and on mechanotransduction modeling at different scales and levels of details. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biomechanics and Mechanobiology)
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