Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries

Please always quote using this URN: urn:nbn:de:0297-zib-54339
  • Cardiovascular diseases are one of the major problems in medicine today and the number of patients increases worldwide. To find the most efficient treatment, prior knowledge about function and dysfunction of the cardiovas- cular system is required and methods need to be developed that identify the disease in an early stage. Mathematical modeling is a powerful tool for prediction and investigation of cardiovascular diseases. It has been shown that the Windkessel model, being based on an analogy between electrical circuits and fluid flow, is a simple but effective method to model the human cardiovascular system. In this paper, we have applied parametric local sensitivity analysis (LSA) to a linear elastic model of the arm arteries, to find and rank sensitive param- eters that may be helpful in clinical diagnosis. A computational model for end-to-side anastomosis (superior ulnar collateral anastomosis with posterior ulnar recurrent, SUC-PUR) is carried out to study the effects of some clinically relevant haemodynamic parameters like blood flow resistance and terminal re- sistance on pressure and flow at different locations of the arm artery. In this context, we also discuss the spatio-temporal dependency of local sensitivities. The sensitivities with respect to cardiovascular parameters reveal the flow resistance and diameter of the vessels as most sensitive parameters. These parameters play a key role in diagnosis of severe stenosis and aneurysms. In contrast, wall thickness and elastic modulus are found to be less sensitive.

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Author:R. Gul, Ch. Schütte, S. Bernhard
Document Type:ZIB-Report
Tag:Windkessel model; anastomosis; cardiovascular parameters; computational cardiovascular model; sensitivity analysis
MSC-Classification:70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Gxx General models, approaches, and methods [See also 37-XX] / 70G60 Dynamical systems methods
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Bxx Controllability, observability, and system structure / 93B35 Sensitivity (robustness)
Date of first Publication:2015/04/07
Series (Serial Number):ZIB-Report (15-22)

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