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

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.

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

2013 ◽  
Vol 305 (12) ◽  
pp. H1709-H1717 ◽  
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.

Development of a Computational Model of Lymphangions in Series: A Parameter Sensitivity Analysis

2011 ◽  
Author(s):  
Jon Weimer ◽  
James E. Moore ◽  
Christopher D. Bertram ◽  
Will Richardson ◽  
Beth Ann Placette
Keyword(s):  
Transport Mechanism ◽  
Lymphatic System ◽  
Vital Role ◽  
The Body ◽  
Negative Events ◽  
Parameter Sensitivity Analysis ◽  
Protein Balance ◽  
Venous Circulation ◽  
In Series ◽  
Normal Health

The lymphatic system plays a vital role in the body to maintain normal health. The lymphatics are responsible for fluid and protein balance, as they transport approximately 3.6 liters/day of fluid from the interstitial spaces to the venous circulation. Throughout this transfer process, both positive and negative events can occur. Undesirable pathogens are typically destroyed in lymph nodes, but since it serves as the primary transport mechanism for the immune system, it is also involved in the spread of pathogens such as cancer cells.

Parameter Sensitivity Analysis of a Large-Scale System With Several Components Interacting in Series

1989 ◽  
Author(s):  
H. Torab
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Optimization Problems ◽  
Parameter Sensitivity ◽  
Engineering Optimization ◽  
Parameter Sensitivity Analysis ◽  
Large Scale Systems ◽  
In Series ◽  
Special Case ◽  
Engineering Optimization Problems

Abstract Parameter sensitivity for large-scale systems that include several components which interface in series is presented. Large-scale systems can be divided into components or sub-systems to avoid excessive calculations in determining their optimum design. Model Coordination Method of Decomposition (MCMD) is one of the most commonly used methods to solve large-scale engineering optimization problems. In the Model Coordination Method of Decomposition, the vector of coordinating variables can be partitioned into two sub-vectors for systems with several components interacting in series. The first sub-vector consists of those variables that are common among all or most of the elements. The other sub-vector consists of those variables that are common between only two components that are in series. This study focuses on a parameter sensitivity analysis for this special case using MCMD.

scholarly journals Sensitivity Analysis of the Transmission Chain of a Horizontal Machining Tool Axis to Design and Control Parameters

2014 ◽  
Vol 6 ◽  
pp. 169064 ◽  
Author(s):  
Stefano Mauro ◽  
Stefano Pastorelli ◽  
Tharek Mohtar
Keyword(s):  
Sensitivity Analysis ◽  
Lumped Parameter Model ◽  
Control Parameters ◽  
Damping Coefficients ◽  
Transmission Chain ◽  
Lumped Parameter ◽  
Tool Axis ◽  
Optimal Value ◽  
Structural Parts ◽  
And Control

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.

Highly Reduced Lumped Parameter Models Representing Impedance Functions at the Interface of One-Dimensional Viscoelastic Continua

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Masato Saitoh
Keyword(s):  
Degrees Of Freedom ◽  
Reaction Force ◽  
Lumped Parameter Model ◽  
Computational Time ◽  
Dynamic Problems ◽  
Modal Expansion ◽  
Mass Element ◽  
Lumped Parameter ◽  
In Series ◽  
Impedance Functions

In recent dynamic problems dealing with high-frequency excitations, such as ultrasonic vibrations, a proper representation of rods transmitting kinetic energy from the interface attached to the vibrating system to the other end is strongly demanded for effectively reducing computational time and domain. A highly reduced lumped parameter model that properly simulates the dynamic characteristics of a uniform, isotropic, homogeneous, and viscoelastic rod subjected to excitations at its end is proposed in this paper. The model consists of springs, dashpots, and so called “gyro-mass elements.” The gyro-mass element generates a reaction force proportional to the relative acceleration of the nodes between which it is placed. This model consists of units arranged in series, each unit consisting of a spring, a dashpot, and a gyro-mass element arranged in parallel. A formula is proposed for determining the properties of the elements in the units based on the modal expansion. The results show that a notable reduction of 90% in the degrees of freedom is accomplished with high accuracy by using the proposed model consisting of a set of units associated with modes in a target frequency region and a supplemental unit associated with residual stiffness, which is advantageous for efficient numerical computations in recent dynamic problems.

Initial Steps Toward Development of a Lumped-Parameter Model of the Lymphatic Network

2013 ◽  
Author(s):  
Samira Jamalian ◽  
Christopher D. Bertram ◽  
James E. Moore
Keyword(s):  
Blood Circulation ◽  
Lymphatic Vessel ◽  
Lymphatic System ◽  
Lymphatic Vessels ◽  
The Body ◽  
Lumped Parameter Model ◽  
Circulation System ◽  
Blood Circulation System ◽  
Lumped Parameter ◽  
Lymphatic Network

One of the primary functions of the lymphatic system is maintaining fluid and protein balance in the body. The system holds this balance by collecting about four liters of fluid every day from the interstitial space and returning it back to the subclavian vein. In contrast to the blood circulation system that relies on the heart for pumping, there is no central pump in the lymphatic system. Thus, the transport of viscous fluid against gravity and pressure difference occurs by recruiting extrinsic and intrinsic pumping mechanisms. Extrinsic pumping is the transport of lymph due to the movements outside the lymphatic vessel such as the pulse in blood vessels, whereas the intrinsic pumping is transport of lymph by contraction of lymphatic muscle cells embedded in the walls of lymphatic vessels. Similar to the veins, the bi-leaflet valves throughout the lymphatic network prevent backflow. Lymphatic valves are biased open and allow for small amounts of back flow before they completely shut.

Effects of Lymphangion Subdivision in a Numerical Model of a Lymphatic Vessel

2011 ◽  
Author(s):  
Christopher D. Bertram ◽  
Charles Macaskill ◽  
James E. Moore
Keyword(s):  
Smooth Muscle ◽  
Numerical Model ◽  
Lymphatic Vessel ◽  
Smooth Muscle Contraction ◽  
Lumped Parameter Model ◽  
Active Tension ◽  
Lumped Parameter ◽  
Pumping Efficiency ◽  
In Series ◽  
Passive Compression

We have recently reported development of a lumped-parameter model for several lymphangions in series [1]. The model provides for both active smooth muscle contraction (intrinsic pumping) and passive compression of the lymphatic by external tissues (extrinsic pumping). The valves which define the lymphangions vary their resistance sigmoidally, having a high (low) resistance for an adverse (favorable) pressure difference. With no refractory period between sinusoidal active tension episodes, maximum pumping efficiency was reached when each lymphangion contracted 135° after that immediately upstream; simultaneous contraction (corresponding to the situation of extrinsic pumping) was especially inefficient.

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

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.

scholarly journals A multiscale sliding filament model of lymphatic muscle pumping

2021 ◽  
Author(s):  
Christopher J. Morris ◽  
David C. Zawieja ◽  
James E. Moore
Keyword(s):  
Smooth Muscle ◽  
Interstitial Fluid ◽  
Cellular Level ◽  
Calcium Oscillations ◽  
Lumped Parameter Model ◽  
Maximum Efficiency ◽  
Lumped Parameter ◽  
Muscle Types ◽  
Lymphatic Pumping ◽  
The Relationship

AbstractThe lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255–318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667–2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

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