Empirical Relationships for the Terminal Settling Velocity of Spheres in Cylindrical Columns

Kehlenbeck, Ralf; Felice, Renzo Di

doi:10.1002/(sici)1521-4125(199904)22:4<303::aid-ceat303>3.0.co;2-8

Cited by 48 publications

(32 citation statements)

References 6 publications

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“…Many wall effect correlations exist covering many Reynolds numbers ranges. In [30], correlations working for Reynolds numbers from 0.01 to 10 000 are proposed by Kehlenbeck and Di Felice. These correlations are very useful to define design rules in the cardiovascular system where .…”

Section: Theoretical Modelmentioning

confidence: 99%

Method of Propulsion of a Ferromagnetic Core in the Cardiovascular System Through Magnetic Gradients Generated by an MRI System

Mathieu

Beaudoin

Martel

2006

IEEE Trans. Biomed. Eng.

219

128

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Abstract-This paper reports the use of a magnetic resonance imaging (MRI) system to propel a ferromagnetic core. The concept was studied for future development of microdevices designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascular system. A mathematical model is described taking into account various parameters such as the size of blood vessels, the velocities and viscous properties of blood, the magnetic properties of the materials, the characteristics of MRI gradient coils, as well as the ratio between the diameter of a spherical core and the diameter of the blood vessels. The concept of magnetic propulsion by MRI is validated experimentally by measuring the flow velocities that magnetized spheres (carbon steel 1010/1020) can withstand inside cylindrical tubes under the different magnetic forces created with a Siemens Magnetom Vision 1.5 T MRI system. The differences between the velocities predicted by the theoretical model and the experiments are approximately 10%. The results indicate that with the technology available today for gradient coils used in clinical MRI systems, it is possible to generate sufficient gradients to propel a ferromagnetic sphere in the larger sections of the arterial system. In other words, the results show that in the larger blood vessels where the diameter of the microdevices could be as large as a couple a millimeters, the few tens of mT/m of gradients required for displacement against the relatively high blood flow rate is well within the limits of clinical MRI systems. On the other hand, although propulsion of a ferromagnetic core with diameter of 600 m may be possible with existing clinical MRI systems, gradient amplitudes of several T/m would be required to propel a much smaller ferromagnetic core in small vessels such as capillaries and additional gradient coils would be required to upgrade existing MRI systems for operations at such a scale.

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Section: Theoretical Modelmentioning

confidence: 99%

Method of Propulsion of a Ferromagnetic Core in the Cardiovascular System Through Magnetic Gradients Generated by an MRI System

Mathieu

Beaudoin

Martel

2006

IEEE Trans. Biomed. Eng.

219

128

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“…where A is the frontal area, the drag coefficient C d is given by [17], β is a dimensionless ratio related to the wall effect caused by the partial vessel occlusion by the robot [18], and v denotes the relative velocity between the robot and the fluid. η and ρ f denote respectively the blood viscosity and density.…”

Section: A Forces 1) Hydrodynamic Drag Forcementioning

confidence: 99%

Observer-based controller for microrobot in pulsatile blood flow

Sadelli

Fruchard

Ferreira

2014

53rd IEEE Conference on Decision and Control

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Abstract-We propose an observer-based controller for a magnetic microrobot immersed in the human vasculature. The drag force depends on the pulsatile blood velocity and specially acts on the microrobot dynamics. In the design of advanced control laws, the blood velocity is usually assumed to be known or set to a constant mean value to achieve the control objectives, whereas the sole robot position is measured. We prove the stability of the proposed observer-based controller combining a backstepping controller with a mean value theorem (MVT) based observer. The resulting estimation of the blood velocity is then illustrated and compared to high gain observer results through simulations.

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“…[28], and C d (Re, β) is the drag coefficient [27]. The non-Newtonian behavior of blood is addressed using [29].…”

Section: A Hydrodynamic Drag Forcementioning

confidence: 99%

Adaptive Controller and Observer for a Magnetic Microrobot

2013

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Abstract-The present paper discusses the control design of a magnetically-guided microrobotic system in blood vessels to perform minimally invasive medical procedures. Such microrobots consist of a polymer binded aggregate of nanosized ferromagnetic particles and a possible payload that can be propelled by the gradient coils of a magnetic device. A fine modeling is developed and used to define an optimal trajectory which minimizes the control efforts. We then synthesize an adaptive backstepping law that ensures a Lyapunov stable and fine tracking despite modeling errors and estimates some key uncertain parameters. As the controller synthesis uses the microrobot unmeasured velocity, the design of a high gain observer is also addressed. Simulations and experiment illustrate the robustness to both noise measurement and some uncertain physiological parameters for a 250µm radius microrobot navigating in a fluidic environment.Index Terms-Magnetic microrobot, nonlinear modeling, adaptive backstepping, high gain observer, noise and parametric uncertainties.

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Empirical Relationships for the Terminal Settling Velocity of Spheres in Cylindrical Columns

Cited by 48 publications

References 6 publications

Method of Propulsion of a Ferromagnetic Core in the Cardiovascular System Through Magnetic Gradients Generated by an MRI System

Method of Propulsion of a Ferromagnetic Core in the Cardiovascular System Through Magnetic Gradients Generated by an MRI System

Observer-based controller for microrobot in pulsatile blood flow

Adaptive Controller and Observer for a Magnetic Microrobot

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