Analysis of Venous Blood Flow and Deformation in the Calf under External Compression

Abstract

Deep vein thrombosis (DVT) is a common post-operative complication, and a serious threat to the patient’s general recovery. In recent years, there has been increasing awareness of the risk of DVT in healthy individuals after prolonged immobility, such as people taking long-period flights or sitting at a computer. Mechanical methods of DVT prophylaxis, such as compression stockings, have gained widespread acceptance, but the haemodynamic mechanism of their action is still not well understood. In this study, computational modelling approaches based on magnetic resonance (MR) images are used to (i) predict the deformation of calf and deep veins under external compression, (ii) determine blood flow and wall shear stress in the deep veins of the calf, and (iii) quantify the effect of external compression on flow and wall shear stress in the deep veins. As a first step, MR images of the calf obtained with and without external compression were analysed, which indicated different levels of compressibility for different calf muscle compartments. A 2D finite element model (FEM) with specifically tailored boundary conditions for different muscle components was developed to simulate the deformation of the calf under compression. The calf tissues were described by a linear elastic model. The simulation results showed a good qualitative agreement with the measurements in terms of deep vein deformation, but the area reduction predicted by the FEM was much larger than that obtained from the MR images. In an attempt to improve the 2D FEM, a hyperelastic material model was employed and a finite element based non-rigid registration algorithm was developed to calculate the bulk modulus of the calf tissues. Using subject-specific bulk modulus derived with this method together with a hyperelastic material model, the numerical results showed better quantitative agreement with MR measured deformations of deep veins and calf tissues. In order to understand the effect of external compression on flow in the deep veins, MR imaging and real-time flow mapping were performed on 10 healthy volunteers before and after compression. Computational fluid dynamics was then employed to calculate the haemodynamic wall shear stress (WSS), based on the measured changes in vessel geometry and flow waveforms. The overall results indicated that application of the compression stocking led to a reduction in both blood flow rate and cross sectional area of the peroneal veins in the calf, which resulted in an increase in WSS, but the individual effects were highly variable. Finally, a 3D fluid-structure interactions (FSI) model was developed for a segment of the calf with realistic geometry for the calf muscle and bones but idealised geometry for the deep vein. The hyperelastic material properties evaluated previously were employed to describe the solid behaviours. Some predictive ability of the FSI model was demonstrated, but further improvement and validation are still needed.