The Computational Modelling of Collecting Lymphatic Vessels

Abstract

This thesis details a 1-d model of a lymphatic vessel, developed from a model by Reddy. Some additions to the modelling techniques were found to be necessary to prevent numerical phenomena not found in experiment. Furthermore the details of the wall and valve were important to the mechanics of the system. This developed model presents flow characteristics which are not represented in the existing lumped parameter or 1-d models of the lymphatic system. Additional terms allow more realistic representation of some modes of flow such as those occurring during collapse. The model was validated using Poiseuille flow calculations and experimental work. Features found in experiment were reproduced in the model. Such as the shark tooth shape of the radius time graph.

A study of the sensitivity of the model to experimental parameters was performed. Features that increased flow included: increased compliance of the vessel, a larger diameter, amplitude of contraction or frequency, or a faster contraction wave.

A lumped parameter model, relating the radius directly to the pressure, was investigated but this did not reproduce flow features such as the shark tooth shaped radius with time relationship or the radius peak at the beginning of a contraction or passive relaxation of the vessel. In the 1-d model the time constant of this passive relaxation increased with the magnitude of contraction. This value may have physiological relevance.