Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

This paper reports how a numerical controlled machine axis was studied through a lumped parameter model. Firstly, a linear model was derived in order to apply a modal analysis, which estimated the first mechanical frequency of the system as well as its damping coefficients. Subsequently, a nonlinear system was developed by adding friction through experimentation. Results were validated through the comparison with a commercial servoaxis equipped with a Siemens controller. The model was then used to evaluate the effect of the stiffness of the structural parts of the axis on its first natural frequency. It was further used to analyse precision, energy consumption, and axis promptness. Finally a cost function was generated in order to find an optimal value for the main proportional gain of the position loop.

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Parameter Sensitivity Analysis of a Lumped-Parameter Model of Lymphangions in Series

ASME 2012 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2012-80849 ◽

2012 ◽

Author(s):

Samira Jamalian ◽

James E. Moore ◽

Christopher D. Bertram ◽

Will Richardson

Keyword(s):

Sensitivity Analysis ◽

Interstitial Fluid ◽

Lymphatic System ◽

Lumped Parameter Model ◽

Node Dissection ◽

Parameter Sensitivity Analysis ◽

Protein Balance ◽

Vital Functions ◽

Lumped Parameter ◽

In Series

The lymphatic system is responsible for vital functions in the human body. In particular, it plays an important role in the immune system mechanism whereby undesirable elements are destroyed in the lymph nodes. But cancer cells also spread via the lymphatic system. The system maintains fluid and protein balance by gathering approximately 4 L/day of interstitial fluid and returning it to the venous system. Lymphedema, an ailment of the system for which there is no known cure, primarily affects cancer patients who have undergone lymph node dissection [1]. To understand how to treat such pathologies of the lymphatic system, it is first necessary to examine its fluid flow and pumping mechanisms quantitatively.

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Parameter sensitivity analysis of a lumped-parameter model of a chain of lymphangions in series

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00403.2013 ◽

2013 ◽

Vol 305 (12) ◽

pp. H1709-H1717 ◽

Cited By ~ 25

Author(s):

Samira Jamalian ◽

Christopher D. Bertram ◽

William J. Richardson ◽

James E. Moore

Keyword(s):

Sensitivity Analysis ◽

Flow Rate ◽

Pressure Difference ◽

Lymphatic System ◽

Lumped Parameter Model ◽

Average Flow Rate ◽

Average Flow ◽

Lumped Parameter ◽

Time Average ◽

A Chain

Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no effective cure for lymphedema, partly because predictive knowledge of lymphatic system reactions to interventions is lacking. A well-developed model of the system could greatly improve our understanding of its function. Lymphangions, defined as the vessel segment between two valves, are the individual pumping units. Based on our previous lumped-parameter model of a chain of lymphangions, this study aimed to identify the parameters that affect the system output the most using a sensitivity analysis. The system was highly sensitive to minimum valve resistance, such that variations in this parameter caused an order-of-magnitude change in time-average flow rate for certain values of imposed pressure difference. Average flow rate doubled when contraction frequency was increased within its physiological range. Optimum lymphangion length was found to be some 13–14.5 diameters. A peak of time-average flow rate occurred when transmural pressure was such that the pressure-diameter loop for active contractions was centered near maximum passive vessel compliance. Increasing the number of lymphangions in the chain improved the pumping in the presence of larger adverse pressure differences. For a given pressure difference, the optimal number of lymphangions increased with the total vessel length. These results indicate that further experiments to estimate valve resistance more accurately are necessary. The existence of an optimal value of transmural pressure may provide additional guidelines for increasing pumping in areas affected by edema.

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STUDY OF UNCERTAINTIES ON A 0D MODEL OF THE SYSTEMIC CIRCULATION

Revista Mundi Engenharia Tecnologia e Gestão (ISSN 2525-4782) ◽

10.21575/25254782rmetg2020vol5n21152 ◽

2020 ◽

Vol 5 (2) ◽

Author(s):

Gilmar Ferreira Da Silva Filho ◽

Rafael Alves Bonfim De Queiroz ◽

Luis Paulo Da Silva Barra ◽

Bernardo Martins Rocha

Keyword(s):

Sensitivity Analysis ◽

Computational Models ◽

Clinical Decision Making ◽

Systemic Circulation ◽

Lumped Parameter Model ◽

Patient Specific ◽

Accurate Estimation ◽

Clinical Patient ◽

Lumped Parameter ◽

Input Parameters

Cardiovascular system is intensely researched to understand the intricate nature of the heart and blood circulation. Nowadays we have well evolved computational models which are useful in many ways for the understanding and analysis of physiological and pathophysiological conditions of the heart. However, the practical use of these models and their results for clinical decision making in specific patients is not straightforward. In this context, models predictions must be accurate and reliable, which can be assessed by quantification of uncertainties in the predictions and sensitivity analysis of the input parameters. Lumped parameter models for the cardiovascular physiology can provide useful data for clinical patient-specific applications. However, the accurate estimation of all parameters of these models is a difficult task, and therefore the determination of the most sensitive parameters is an important step towards the calibration of these models. We perform uncertainty quantification and sensitivity analysis based on generalised polynomial chaos expansion in a lumped parameter model for the systemic circulation. The objective of this work is to verify the effect of uncertainties from input parameters on the predictions of the models and to identify parameters that contribute significantly to relevant quantities of interest. Numerical experiments are performed and results indicate a set of the most relevant parameters in the context of these models.

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Sensitivity analysis of a lumped-parameter model for infiltration

Journal of Hydrology ◽

10.1016/0022-1694(84)90235-x ◽

1984 ◽

Vol 67 (1-4) ◽

pp. 97-113

Author(s):

Kim Pingoud

Keyword(s):

Sensitivity Analysis ◽

Lumped Parameter Model ◽

Lumped Parameter

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Optimal measurement locations for diagnosis of aortic abnormalities in a lumped-parameter model of the systemic circulation using sensitivity analysis

International Journal of Biomathematics ◽

10.1142/s1793524517501169 ◽

2017 ◽

Vol 10 (08) ◽

pp. 1750116 ◽

Cited By ~ 2

Author(s):

R. Gul ◽

S. Bernhard

Keyword(s):

Sensitivity Analysis ◽

Systemic Circulation ◽

The Body ◽

Lumped Parameter Model ◽

Aorta Ascendens ◽

Optimal Measurement ◽

Linear Elastic ◽

Lumped Parameter ◽

Basic Theme ◽

Cardiovascular Simulator

The basic theme of this work is to identify the optimal measurement locations for pressure and flow in the systemic circulation to detect aortic stenoses and aneurysms in early stages of a disease. For this purpose, a linear elastic lumped parameter model of the fluid dynamical simulator, major arterial cardiovascular simulator (MACSim), is considered and global sensitivity analysis is applied to identify the better measurement locations for pressure and flow in the systemic circulation. The obtained results of sensitivity analysis provide insight that enable the experimentalists to optimize their experimental setups for detecting aortic stenoses and aneurysms using parameter estimation process. From the results, it is observed that the stenosis in the thoracic aorta can be identified from both pressure and flow at the location itself, nearby nodes, aorta ascendens, arcus aorta, arteria subclavia and arteria axillaris. On the other hand, the preferable measurement locations for abdominal aneurysms are locations themselves, nearby nodes and left/right leg of the body.

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