Integrated geometric and mechanical analysis of an image-based lymphatic valve.
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abstract
Lymphatic valves facilitate the lymphatic system's role in maintaining fluid homeostasis. Malformed valves are found in several forms of primary lymphdema, resulting in incurable swelling of the tissues and immune dysfunction. Their experimental study is complicated by their small size and operation in low pressure and low Reynolds number environments. Mathematical models of these structures can give insight and complement experimentation. In this work, we present the first valve geometry reconstructed from confocal imagery and used in the construction of a subject-specific model in a closing mode. A framework is proposed whereby an image is converted into a valve model. An FEA study was performed to identify the significance of the shear modulus, the consequences of smoothing the leaflet surface and the effect of wall motion on valve behaviour. Smoothing is inherent to any analysis from imagery. The nature of the image, segmentation and meshing all cause attenuation of high-frequency features. Smoothing not only causes loss of surface area but also the loss of high-frequency geometric features which may reduce stiffness. This work aimed to consider these effects and inform studies by taking a manual reconstruction and through manifold harmonic analysis, attenuating higher frequency features to replicate lower resolution images or lower degree-of-freedom reconstructions. In conclusion, two metrics were considered: trans-valvular pressure required to close the valve, Pc, and the retrograde volume displacement after closure. The higher Pc, the greater the volume of lymph that will pass through the valve during closure. Retrograde volume displacement after closure gives a metric of compliance of the valve and for the quality of the valve seal. In the case of the image-specific reconstructed valve, removing features with a wavelength longer than four m caused changes in Pc. Varying the shear modulus from 10kPa to 60kPa caused a 3.85-fold increase in the retrograde volume displaced. The inclusion of a non-rigid wall caused Pc to increase from 1.56 to 2.52cmH2O.
