A constitutive modelling framework for applications to in vivo longitudinal data: Evaluation in a 60-day head-down...

Vascular cells continuously remodel the arterial wall (micro)structure in response to changes in their biomechanical/biochemical environment. Although the functional effects of arterial remodelling can be easily measured, assessing the underlying microstructural mechanisms is complex in vivo. Constitutive modelling is a computational technique that allows for linking whole-organ function to tissue constituent-level mechanics. However, the need for comprehensive biomechanical data for model parametrisation hampers its clinical applicability. In the present study, we propose a novel constitutive modelling framework that addresses this limitation by leveraging longitudinal acquisitions of pressure-diameter relationships at different arterial beds to aid model parametrisation. We applied our constitutive framework to data from a study on the effect of 60 days head-down bed rest (HDBR) on arterial function, where pressure-diameter relationships of three arteries (carotid, femoral and popliteal) were measured at baseline, during HDBR (two time points) and during a 30-day recovery (two time points). We modelled the arterial wall as a constrained mixture of elastin, collagen and vascular smooth muscle cells (VSMCs). The dimensionality of the parameterisation problem was reduced through assumptions on (i) the time evolution of the behaviour of individual constituents and (ii) consistency in intrinsic constituent mechanical properties across different arterial beds. Overall, the proposed framework captured well the in vivo data (R² = 0.89 ± 0.05). We identified increased VSMC contraction and microstructural re-arrangement of collagen fibres as key adaptations to haemodynamic changes during HDBR, also resulting in reversible de-stiffening of peripheral arteries. The proposed approach appears promising for disentangling microstructural mechanisms of arterial remodelling in clinical settings. KEY POINTS: Constitutive modelling is a computational technique that links the macroscopic behaviour of arteries to the microstructure and mechanics of the constituents of their wall. Although constitutive modelling is used extensively on ex vivo data, the sparsity of biomechanical data that can be acquired in vivo hinders its applicability in clinical settings, where it could be instrumental in disentangling remodelling processes in ageing and disease. We propose a novel framework that leverages longitudinal acquisition of arterial waveforms at different arterial sites to aid in the parametrisation of comprehensive constitutive models. We exemplify the utility of our approach by teasing out the pivotal adaptation roles of vascular smooth muscle cell contraction and collagen microstructural remodelling in response to haemodynamic alterations resulting from prolonged head-down bed rest. Our approach shows promise for the quantitative characterisation of arterial remodelling from non-invasive in vivo data that can be easily measured in clinical settings.