A Musculoskeletal Model of the Equine Forelimb for Determining Surface Stresses and Strains in the Humerus—Part II. Experimental Testing and Model Validation

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Sarah Pollock ◽  
Susan M. Stover ◽  
M. L. Hull ◽  
Larry D. Galuppo
Keyword(s):  
Mathematical Model ◽  
Stress Fracture ◽  
Biceps Brachii ◽  
Experimental Testing ◽  
Longitudinal Axis ◽  
Principal Strain ◽  
Longitudinal Strains ◽  
The Mathematical Model ◽  
Experimental Strains

The first objective of this study was to experimentally determine surface bone strain magnitudes and directions at the donor site for bone grafts, the site predisposed to stress fracture, the medial and cranial aspects of the transverse cross section corresponding to the stress fracture site, and the middle of the diaphysis of the humerus of a simplified in vitro laboratory preparation. The second objective was to determine whether computing strains solely in the direction of the longitudinal axis of the humerus in the mathematical model was inherently limited by comparing the strains measured along the longitudinal axis of the bone to the principal strain magnitudes and directions. The final objective was to determine whether the mathematical model formulated in Part I [Pollock et al., 2008, ASME J. Biomech. Eng., 130, p. 041006] is valid for determining the bone surface strains at the various locations on the humerus where experimentally measured longitudinal strains are comparable to principal strains. Triple rosette strain gauges were applied at four locations circumferentially on each of two cross sections of interest using a simplified in vitro laboratory preparation. The muscles included the biceps brachii muscle in addition to loaded shoulder muscles that were predicted active by the mathematical model. Strains from the middle grid of each rosette, aligned along the longitudinal axis of the humerus, were compared with calculated principal strain magnitudes and directions. The results indicated that calculating strains solely in the direction of the longitudinal axis is appropriate at six of eight locations. At the cranial and medial aspects of the middle of the diaphysis, the average minimum principal strain was not comparable to the average experimental longitudinal strain. Further analysis at the remaining six locations indicated that the mathematical model formulated in Part I predicts strains within ±2 standard deviations of experimental strains at four of these locations and predicts negligible strains at the remaining two locations, which is consistent with experimental strains. Experimentally determined longitudinal strains at the middle of the diaphysis of the humerus indicate that tensile strains occur at the cranial aspect and compressive strains occur at the caudal aspect while the horse is standing, which is useful for fracture fixation.

scholarly journals Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

Viruses ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 547
Author(s):  
Veronika Bernhauerová ◽  
Veronica V. Rezelj ◽  
Marco Vignuzzi
Keyword(s):  
Mathematical Model ◽  
Viral Infection ◽  
Host Cell ◽  
Decay Time ◽  
Zika Virus ◽  
Infectious Virus ◽  
Numerical Characterization ◽  
The Mathematical Model

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

scholarly journals Correlation between Animal and Mathematical Models for Prostate Cancer Progression

2009 ◽  
Vol 10 (4) ◽  
pp. 241-252 ◽  
Author(s):  
Z. Jackiewicz ◽  
C. L. Jorcyk ◽  
M. Kolev ◽  
B. Zubik-Kowal
Keyword(s):  
Mathematical Model ◽  
Cancer Progression ◽  
Growth Rates ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Tumour Progression ◽  
Prostate Cancer Progression ◽  
The Mathematical Model

This work demonstrates that prostate tumour progressionin vivocan be analysed by using solutions of a mathematical model supplemented by initial conditions chosen according to growth rates of cell linesin vitro. The mathematical model is investigated and solved numerically. Its numerical solutions are compared with experimental data from animal models. The numerical results confirm the experimental results with the growth ratesin vivo.

scholarly journals Research on Indentation Rolling Resistance Based on Viscoelasticity of Cover Rubber under a Conveyor Belt

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wenjun Meng ◽  
Lidong Zhou
Keyword(s):  
Mathematical Model ◽  
Normal Force ◽  
Experimental Testing ◽  
Rolling Resistance ◽  
Maxwell Model ◽  
Conveyor Belt ◽  
Belt Conveyor ◽  
Belt Speed ◽  
Indentation Rolling Resistance ◽  
The Mathematical Model

Minimizing the power consumption of the belt conveyor is the common wish of all enterprises and even countries. Among all the resistances generated by the belt conveyor during the operation, the indentation rolling resistance accounts for the largest proportion and the power consumed is the largest. Therefore, accurately predicting and reducing the rolling resistance of indentation is the focus of current research. Firstly, based on the three-element Maxwell solid model, the dynamic loading experiments of cylindrical rubber made of conveyor belt cover material were carried out at different temperatures. The identification models of elastic moduli E2 and E3 and viscosity coefficient η2 in the three-element Maxwell model were obtained, and then the fitting functions of the three parameters were gotten, which can intuitively reflect the influence of temperature. Secondly, the mathematical model of the indentation rolling resistance was derived. The mathematical model is characterized by the direct parameters such as belt speed v, thickness of backing material h, the idler radius R, and the rubber viscoelastic parameters E2, E3, and η2 and the indirect parameters such as normal force P and temperature T. Afterwards, the effects of belt speed, normal force, temperature, idler radius, and thickness of underlay on the indentation rolling resistance were studied under different working conditions. After that, experimental testing and analysis were fulfilled using test equipment and compared with theoretical analysis results. The results prove that the theoretical results are basically consistent with the experimental results, in line with the actual engineering rules. Finally, the application of the results in practical engineering was analyzed superficially.

scholarly journals Experimental and mathematical modelling of magnetically labelled mesenchymal stromal cell delivery

2021 ◽  
Vol 18 (175) ◽  
pp. 20200558
Author(s):  
E. F. Yeo ◽  
H. Markides ◽  
A. T. Schade ◽  
A. J. Studd ◽  
J. M. Oliver ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Magnetic Nanoparticles ◽  
Mathematical Modelling ◽  
Magnetic Targeting ◽  
Cell Capture ◽  
Cell Therapies ◽  
External Magnet ◽  
The Mathematical Model

A key challenge for stem cell therapies is the delivery of therapeutic cells to the repair site. Magnetic targeting has been proposed as a platform for defining clinical sites of delivery more effectively. In this paper, we use a combined in vitro experimental and mathematical modelling approach to explore the magnetic targeting of mesenchymal stromal cells (MSCs) labelled with magnetic nanoparticles using an external magnet. This study aims to (i) demonstrate the potential of magnetic tagging for MSC delivery, (ii) examine the effect of red blood cells (RBCs) on MSC capture efficacy and (iii) highlight how mathematical models can provide both insight into mechanics of therapy and predictions about cell targeting in vivo. In vitro MSCs are cultured with magnetic nanoparticles and circulated with RBCs over an external magnet. Cell capture efficacy is measured for varying magnetic field strengths and RBC percentages. We use a 2D continuum mathematical model to represent the flow of magnetically tagged MSCs with RBCs. Numerical simulations demonstrate qualitative agreement with experimental results showing better capture with stronger magnetic fields and lower levels of RBCs. We additionally exploit the mathematical model to make hypotheses about the role of extravasation and identify future in vitro experiments to quantify this effect.

scholarly journals Experimental and mathematical modelling of magnetically labelled mesenchymal stromal cell delivery

2020 ◽  
Author(s):  
E.F. Yeo ◽  
H. Markides ◽  
A.T. Schade ◽  
A.J. Studd ◽  
J.M. Oliver ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Magnetic Nanoparticles ◽  
Mathematical Modelling ◽  
Magnetic Targeting ◽  
Cell Capture ◽  
Cell Therapies ◽  
External Magnet ◽  
The Mathematical Model

AbstractA key challenge for stem cell therapies is the delivery of therapeutic cells to the repair site. Magnetic targeting has been proposed as a platform for defining clinical sites of delivery more effectively. In this paper we use a combined in vitro experimental and mathematical modelling approach to explore the magnetic targeting of mesenchymal stromal cells (MSCs) labelled with magnetic nanoparticles using an external magnet. This study aims to (i) demonstrate the potential of magnetic tagging for MSC delivery, (ii) examine the effect of red blood cells (RBCs) on MSC capture efficacy and (iii) highlight how mathematical models can provide both insight into mechanics of therapy and predictions about cell targeting in vivo.In vitro MSCs are cultured with magnetic nanoparticles and circulated with RBCs over an external magnet. Cell capture efficacy is measured for varying magnetic field strengths and RBC percentages. We use a 2D continuum mathematical model to represent the flow of magnetically tagged MSCs with RBCs. Numerical simulations demonstrate qualitative agreement with experimental results showing better capture with stronger magnetic fields and lower levels of RBCs. We additionally exploit the mathematical model to make hypotheses about the role of extravasation and identify future in vitro experiments to quantify this effect.

Experimental Testing and Validation of a Magnetorheological (MR) Damper Model

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Weng Wai Chooi ◽  
S. Olutunde Oyadiji
Keyword(s):  
Mathematical Model ◽  
Experimental Testing ◽  
Mr Damper ◽  
Parallel Plates ◽  
Mr Fluids ◽  
Annular Gap ◽  
The University ◽  
University Of Manchester ◽  
The Mathematical Model ◽  
Theoretical Simulations

The focus of this paper is on the experimental validation of a mathematical model that was developed for the flow of magnetorheological (MR) fluids through the annular gap in a MR damper. Unlike previous work by other researchers, which approximate the flow of the MR fluid through this annulus as a flow of fluid through two infinitely wide parallel plates, the model presented represents accurately the annular flow. In this paper, the mathematical model is validated via experimental testing and analysis of a double-tube MR damper fabricated at the University of Manchester, UK. The experimental setup and the procedures for executing the tests on the MR damper according to established standards for the testing of conventional automotive dampers are given. This involved sets of many isofrequency sinusoidal tests of various displacement amplitudes. Predictions from theoretical simulations based on the mathematical model are validated using the data collected from the experiments. It was found that the modeling procedure represents the MR damper very satisfactorily.

scholarly journals TNF-α increases endothelial progenitor cell adhesion to the endothelium by increasing bond expression and affinity

2015 ◽  
Vol 308 (11) ◽  
pp. H1368-H1381 ◽  
Author(s):  
Anthony R. Prisco ◽  
Michael R. Prisco ◽  
Brian E. Carlson ◽  
Andrew S. Greene
Keyword(s):  
Mathematical Model ◽  
Cell Adhesion ◽  
Flow Chamber ◽  
Target Tissue ◽  
Endothelial Progenitor ◽  
Tnf Α ◽  
Late Antigen ◽  
Factor Α ◽  
The Mathematical Model

Endothelial progenitor cells (EPCs) are a rare population of cells that participate in angiogenesis. To effectively use EPCs for regenerative therapy, the mechanisms by which they participate in tissue repair must be elucidated. This study focused on the process by which activated EPCs bind to a target tissue. It has been demonstrated that EPCs can bind to endothelial cells (ECs) through the tumore necrosis factor-α (TNF-α)-regulated vascular cell adhesion molecule 1/very-late antigen 4 (VLA4) interaction. VLA4 can bind in a high or low affinity state, a process that is difficult to experimentally isolate from bond expression upregulation. To separate these processes, a new parallel plate flow chamber was built, a detachment assay was developed, and a mathematical model was created that was designed to analyze the detachment assay results. The mathematical model was developed to predict the relative expression of EPC/EC bonds made for a given bond affinity distribution. EPCs treated with TNF-α/vehicle were allowed to bind to TNF-α/vehicle-treated ECs in vitro. Bound cells were subjected to laminar flow, and the cellular adherence was quantified as a function of shear stress. Experimental data were fit to the mathematical model using changes in bond expression or affinity as the only free parameter. It was found that TNF-α treatment of ECs increased adhesion through bond upregulation, whereas TNF-α treatment of EPCs increased adhesion by increasing bond affinity. These data suggest that injured tissue could potentially increase recruitment of EPCs for tissue regeneration via the secretion of TNF-α.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

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